A particular type of mouse's weights are normally distributed, with a mean of 359 grams and a standard deviation of 33 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places)
a) What is the probability that the mouse weighs less than 405 grams?
b) What is the probability that the mouse weighs more than 461 grams?
c) What is the probability that the mouse weighs between 406 and 461 grams?
d) Is it unlikely that a randomly chosen mouse would weigh less than 405 grams?
i. No, the likelihood exceeds 50%
ii. No, the likelihood exceeds 5%
iii. Yes, the likelihood is less than 50%
iv. Yes, the likelihood is less than 5%
e) What is the cutoff for the heaviest 10% of this type of mouse?

Answers

Answer 1

Answer:

Following are the responses to the given points:

Step-by-step explanation:

Given:

[tex]\mu = 359 \ \ \ \ \ \sigma = 33\\\\[/tex]

Using formula:

[tex]\to P(X = x) = P\left ( z < \frac{x-\mu }{\sigma } \right )[/tex]

For point a:

[tex]\to x= 406\\\\P(X < 406 ) = P\left ( z < \frac{406-359 }{33 } \right )\\\\[/tex]

                   [tex]= P\left ( z <1.4242\right )\\\\= 0.9222[/tex]

For point b:

[tex]\to x= 461\\\\P(X > 461 ) = P\left ( z > \frac{461 -359 }{33 } \right )\\\\[/tex]

                   [tex]= 1 - P\left ( z < 3.0909 \right )\\\\= 1 - 0.9990\\\\= 0.0001[/tex]

For point c:

[tex]\to x= 406\ \ and \ \ 461\\\\P(406 <X < 461 ) = P(X < 461) - P (X < 406)\\\\[/tex]

                              [tex]= 0.9990 - 0.9222\\\\= 0.0768\\\\[/tex]

For point d:

[tex]P(X < 406) = 0.9222 = 92.22 \%\ that \ is \ greater \ than\ 50\%[/tex]

Hence, the correct choice is "i".

For point e:

[tex]\to P(X > z) = 0.1\\\\\to 1 - P(X < z) = 0.1\\\\\to P(\frac{x-\mu }{\sigma }) = 0.9\\\\\to \frac{x-359}{33 } = 1.28\\\\ \to x = 401.24\\\\[/tex]


Related Questions

Please can somebody help me please!

Answers

Answer:

h = 12 ft

Step-by-step explanation:

Area of a rectangle formula:

A = bh

Given:

A = 24b

b = 2b

Work:

A = bh

24b = 2b(h)

h = (24b)/(2b)

h = 12

Can someone help me with think fast?

Answers

Answer:

124

Step-by-step explanation:

A supplementary angle is 180

180-56=124

124 is the answer hope this helps

Help please!!!!!!!!!!!!!!!

Answers

Answer:

-1, 5

Step-by-step explanation:

no really explanation, but its a graph and when u have agraph x goes before y. and the x in the middle of it is what its talking about and u can see the middle is on a 5 and a -1

chhering deposite rs. 40000 in a bank at the rate of 5% p.a. if he has to pay 5%of the total interest as tax for the bank how much will he get after 4 years​

Answers

Answer: Rs 7600

Step-by-step explanation:

The interest will be calculated as:

= Principal × Rate × Time

= 40000 × 5% × 4

= 40000 × 0.05 × 4

= 8000

Since he has to pay 5% of the total interest as tax for the bank, the amount that he will he get after 4 years will be:

= 8000 - (5% × 8000)

= 8000 - (0.05 × 8000)

= 8000 - 400

= 7600

Therefore, he'll get Rs 7600

The midpoint of the coordinates (9, 11) and (7,8) is​

Answers

Answer:

The midpoint: (8,9.5)

Step-by-step explanation:

((9+7)/2,(11+8)/2))

Find the volume. If you have any problems please tell me thank you.

Answers

Answer:

Step-by-step explanation:

Formula = V = l x w x h

V = 4.25 x 2.75 x 5

V = 58.438 --> 58.44

Will give Brainly plz answer fast

Answers

Answer:

sr for messy handwriting

please help asap thanks

Answers

Answer:

All functions are relations

Step-by-step explanation:

You saved $200 on your new laptop because you bought it online. If this was a 20% savings from the original price, find the original cost of the lapto

Answers

Answer:

$1000

Step-by-step explanation:

$200 was saved on a new laptop

This was 20% of the original price of the laptop

Therefote the original cost of the laptop can be calculated as follows

= 20/100x = 200

= 0.2x= 200

Divide both sides by the coefficient of x which is 0.2

x= 200/0.2

= 1000

Hence the original cost of the laptop is $1000

Ivan and Tanya share £150 in the ratio 4 : 1
Work out how much more Ivan gets compared to Tanya.

Answers

Answer:

£90 more

Step-by-step explanation:

4+1=5

150/5=30

I:T

4:1 ×30

120:30

120-30=90

The cost of 3 pounds of grapes is $9.75. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of grapes, x? pls help, its due by the end of the day (3 pm)

Answers

Answer:

3.75

Step-by-step explanation:

We can write a ratio to solve

3 lbs             x lbs

---------- = -----------

9.75            y dollars

Using cross products

3y = 9.75 x

Divide each side by 3

3y/3 = 9.75x/3

y =3.75x

The constant is 3.75

Write an explicit formula for an, the nth term of the sequence 1, 11, 21

Answers

Answer:

an = 10n - 9.

Step-by-step explanation:

This is arithmetic with first term a1 = 1 and common difference 10.

an = a1 + d(n-1)

= 1 + 10(n - 1)

= 1 + 10n - 10

= 10n - 9.

a rectangular garden measures 300m by 460m. what is the perimeter of the garden ? in metres?​

Answers

Answer:

hgvjkhy88ubuybyi

Step-by-step explanation:

hjuoihgvgbhko

An automobile insurance company divides customers into three risk categories: Good (G), Medium (M), and Poor (P). Assume the following distribution of customers: 70% are Good risks, 20% are Medium risks, and 10% are Poor risks. Assume that the probabilities of a customer filing an accident claim (C) in the course of a year are: 0.5% for Good, 1% for Medium, and 2.5% for Poor. A customer is chosen at random.
a) What is the probability that the customer is a good risk and has filed a claim?b) What is the probability that the customer has filed a claim?c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

Answers

Answer:

a) 0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

b) 0.0395 = 3.95% probability that the customer has filed a claim.

c) 0.8861 = 88.61% probability that the customer is a good risk

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that the customer is a good risk and has filed a claim?

70% are good risks.

Of those, 0.5% file a claim. So

[tex]0.7*0.05 = 0.035[/tex]

0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

b) What is the probability that the customer has filed a claim?

0.5% of 70%(good risks)

1% of 20%(medium risks)

2.5% of 10%(poor risks). So

[tex]0.05*0.7 + 0.01*0.2 + 0.025*0.1 = 0.0395[/tex]

0.0395 = 3.95% probability that the customer has filed a claim.

c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

0.0395 = 3.95% probability that the customer has filed a claim means that [tex]P(A) = 0.0395[/tex]

0.035 = 3.5% probability that a customer is a good risk and has filed a claim means that [tex]P(A \cap B) = 0.035[/tex]

Thus

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035}{0.0395} = 0.8861[/tex]

0.8861 = 88.61% probability that the customer is a good risk

You determined that you can make 72 donuts in 2hours. At rate,how many donuts can you make in 8 hours?

Answers

Answer:

288 donuts

Step-by-step explanation:

Answer:

288 donuts

Step-by-step explanation:

72 divided by 2 is 36 so that means you will make 36 donuts in 1 hour so now we have our unit rate which is 36. so then you multiply 36 by 8 and you get 288. that is your answer

Pls help me ASAP show work please

Answers

Answer:

$3.48 for each pair of socks.

Step-by-step explanation:

It's a little confusing, because it says they're buying 2 socks, but then asks for the price of each of 2 *pairs* of socks. I'm going to believe the first sentence should say they paid for 2 pairs of socks.

They have $10, and get $3.04 in change. So we'll subtract $3.04 from $10 to find out the cost of 2 pairs of socks.

10 - 3.04 = 6.96

Then divide $6.96 by 2 pairs of socks

6.96/2 = $3.48 for each pair of socks.

If 6x=48 find the value of 53-7x (A.) 5 (B) -3 (C) -5 (D) 3

Answers

Answer:

The answer is -3.

Step-by-step explanation:

If 6x=48, the answer for x is 8. And from there, I did 7(8). And then 53-56 and got -3.

The answer is B. -3.

Karen has calls has 500 or 900 yards of thick soft wool, she has 200 feet at the strore they have 500 feet of wool. How many balls should she buy

Answers

Answer:

Yes.

Step-by-step explanation:

Because yes.

A coffee vending machine fills 100 cups of coffee before it has to be refilled. On a Monday, the mean number of ounces filled in a cup of coffee was 7.5. The machine is known to have a standard deviation in filling volume of 0.25 ounces. Find a 99% confidence interval for the mean number of ounces dispensed by this machine.

Answers

Answer:

The 99% confidence interval for the mean number of ounces dispensed by this machine is (7.44, 7.56).

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{0.25}{\sqrt{100}} = 0.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 7.5 - 0.06 = 7.44 ounces.

The upper end of the interval is the sample mean added to M. So it is 7.5 + 0.06 = 7.56 ounces.

The 99% confidence interval for the mean number of ounces dispensed by this machine is (7.44, 7.56).

I have 225 in my account I can spend all but 20%

Answers

Answer:

20 % is 45 so keep this much remaining

Step-by-step explanation:

Answer:

You can spend 80%. Multiple 225 × 0

80. 225×0.80 = 180. Now you will have $180

Step-by-step explanation:

Have a great day and summer.

Find the sum of the geometric series if n = 6, r= 1/4, a = 2.

Answers

Sn = a(1-r^n)/(1-r)

Sn= 2(1-1/4096)/0.75= 2.67

explain or not idc lol

Answers

Answer:

B, 20,000

Step-by-step explanation:

429 X 48 = 20,598

If you estimate, it would be 20,000.

So, there you know B, 20,000 is your answer.

Help&Show ur work plz<3

Answers

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

The chords subtended by equal arcs are equal.

Therefore,

[tex]2x + 4 = 18[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

Hence, value of x = 7

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

PLS HELP THIS IS A TEST

Which number satisfies the inequality below?

1.75x + 4.50 < 20

a: 13
b: 14
c: 9
d: 7

Answers

Answer:

D: 7

Step-by-step explanation:

1.75 (7) + 4.50

12.25 + 4.50

= 16.75

16.75 < 20

Write down the general equation of the normal distribution

Answers

The following is the plot of the normal percent point function. where \phi is the cumulative distribution function of the standard normal distribution and Φ is the probability density function of the standard normal distribution.

92.6% of 738 toy robots on an assembly line will be approved by the quality-control inspector. Write and solve a proportion to find how many robots will be approved.

Answers

Answer: D. n/738 = 92.6/100 ;683 robots

Explantion: cross multiply 738 x 92.6 then divide by 100

Warner was paid $375.25 for working 25 hours. What was his hourly pay?

Answers

Answer:

$15.01 an hour

Step-by-step explanation:

[tex]\frac{375.25}{25}=15.01[/tex]

Justin earns $75 per week . How much does he earn in 30 weeks

Answers

the answer is $2,250

Answer:

$2,250

Step-by-step explanation:

$75=1 week

$75×30=$2,250

Which of the following is the solution to this system of equations?
-2x + 3y = 18
x = -y + 1
Possible answers
No solution Infinite solution 4,-3 -3,4

Answers

Answer:

-3, 4

Step-by-step explanation:

__________________

which of the following is equivalent to (5-7i)(5-7i)

Answers

Answer:

Step-by-step explanation:

Here we are multiplying together two complex numbers which happen to be identical:  both are 5 - 7i).

This is also "the square of 5 - 7i:  (5 - 7I)^2

In both cases, the result is 25 - 35i - 35i - 49, or 74 - 70i

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