A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 52.5 mm and a standard deviation of 2.5 mm. What percent of the butterflies had the following wingspans? A. Less than 48.9 mm B. Between 49 and 55

Answer:

A. 7.5%

B. 68.26%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 52.5 mm and a standard deviation of 2.5 mm.

This means that [tex]\mu = 52.5, \sigma = 2.5[/tex]

A. Less than 48.9 mm

The proportion is the pvalue of Z when X = 48.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{48.9 - 52.5}{2.5}[/tex]

[tex]Z = -1.44[/tex]

[tex]Z = -1.44[/tex] has a pvalue of 0.075

0.075*100% = 7.5%, which is the answer.

B. Between 49 and 55

The proportion is the pvalue of Z when X = 55 subtracted by the pvalue of Z when X = 49. So

X = 55

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55 - 52.5}{2.5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

X = 49

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 52.5}{2.5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26%, which is the answer.

The percent of the butterflies had the given wingspans are;

A) 7.5%

B) 76.64%

We are given;

Population mean; μ = 52.5 mm

Population standard deviation; σ = 2.5 mm

Formula for z-score is;

z = (x' - μ)/σ

A) For less than 48.9 mm,P(X' < 48.9);

z = (48.9 - 52.5)/2.5

z = -1.44

From online p-value from z-score calculator, we have;

P(X' < 48.9) = 0.075 or 7.5%

B) For x' between 49 and 55, P(49 < X < 55)

At x' = 49;

z = (49 - 52.5)/2.5

z = -1.4

Z-score at x' = 55;

z = (55 - 52.5)/2.5

z = 1

From online p-value from z-score calculator, the p-value between the two z-scores is;

p = 0.7664 or 76.64%

Read more about z-scores at; https://brainly.com/question/6316394

The cost of interest of a $500 loan for 12 months is $21.88. What is the
interest rate charged for the loan per year?

John put $3,000 in his savings at 2% annually for 3 years. What did he earn in simple interest? A $60 B. $180 O c $600 OD. $1,800​

express using exponents 10^8x10^4=

Ben is throwing a ball across a 48-yard field. He threw it of the way across the field. How far did Ben throw the ball?

Find the x
please will give brainliest

PLEASE HELP ASAP WILL GIVE BRANLIESTKayla is installing a rectangular play area in her backyard so her new puppy can run around. After installing 42 feet of fence for the play area, she still has 12 feet of fence left to install. 12 + p = 42 or p - 42 = 12
Let p represent the perimeter of the play area. Which equation models the problem?
Solve this equation to find the perimeter of the play area.
_____________ feet

How many fewer hot dogs were sold on Wednesday than Tuesday?

Pls help me cri I'm almost done and it's 2 am

I apologize for the messy photo but please help me with this, I’m really confused! Thank you so so so much.

11 points pls help moby max

WILL MARK BRAINLIEST W 20 POINTS
What is most likely the line of best fit for this scatter plot? Graph shows numbers from 0 to 14 at increments of 1 on the x axis and numbers from 0 to 22 at increments of 2 on the y axis. Scatter plot shows ordered pairs 1, 4 and 2, 7 and 3, 9 and 4, 10 and 5, 10 and 6, 12 and 7, 14 and 8, 15 and 9, 16 and 10, 18 and 11, 20 and 12, 22. A line labeled A joins ordered pair 0, 2.5 and 12.5, 22. A line labeled B joins ordered pairs 0, 3.5 and 14, 16. A line labeled C joins ordered pairs 0, 3.5 and 14, 11. A line labeled D joins ordered pairs 0, 4 and 14, 5.5. Line A Line B Line C Line D

What is the mean absolute deviation of each swim club?
A:5
B:50
C:0
D:10

Answer this please. I need it done in 5 minutes ASAP. Thank you

Determine the
circumference
when the
radius is 16.
and please show me how you got the answer​

Please help me with this

Write your answer using integers, proper fractions and improper fractions in the simplest form
PLEASE HELP

I need help this is so hard.

(x^2y^-2)^3/yx^-4 please help

The two cones below are similar. What is the height of the larger cone?

A.
28
—
5

В.
35
—
4

C.
20
—
7

D.
5

Solve for x using
cross multiplication.
2x=4 =
2x – 4
3
x + 1
2
x = [?]
Enter

Augusto wants to prove to his parents that watching TV while he does his homework will help him get better grades. He decides to ask 20 of his friends if they watch TV while they do their homework and what their grades are. He finds that his friends who have high grades also watch TV while they do their homework. He tells his parents that he has proven that watching TV while doing homework will cause his grades to improve. What mistake has Augusto made?

Solve the simultaneous equations
4x+3y=11
2x-y=-2

Simplify the following expression. x(x - 3) - 4(x2 + 7)

Alex, Ben, Chuck, and David all called in to a radio show to get free tickets to a concert. List all the possible orders in which their calls could have been received.​

Write the explicit rule
50, 45, 40, 35, 30

Please? I really need this answer if you can

A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per
tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the
true mean number of suitable apples produced per tree is between 375 and 520 apples. Which of the following can
be accounted for by the margin of error of this interval?
OOO
response bias
nonresponse bias
sampling variation
undercoverage bias

Weather affects flights across the nation, causing delays, cancellations, and general disruption to the NAS. You have gathered a random sample of departures delayed due to weather from your airport (KXYZ) for the month of April through July. You know that across America, weather delayed an average of 59 flights per day (σ =34.83) during that time period. You want to know if weather delays on flights from your airport differ significantly from those across the nation. Your significance level is set at 0.05. Analyze the data below using the correct t-test and be sure to check assumptions of the data.

Answer the following questions:

a. What type of t test should be used to address this research question, and why?
b. What is the null hypothesis?
c. What is the alternative hypothesis?
d. What is the mean and standard deviation for amount of the population?
e. What is the mean and standard deviation for the sample?
f. What are the degrees of freedom? How do you compute it?
g. What is the effect size (Cohen’s d) if applicable?
h. What is the test value?
i. What is the t statistic?

Help I over slept and only have one period to finish this test!!

a stereo system cost $4,800. It depreciates 12% a year. How much is the system worth after 2 years?​