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

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 and standard deviation , the z-score of a measure X is given by:

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

A. Less than 48.9 mm

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

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

has a pvalue of 0.8413

X = 49

has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

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

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|