a. For classes of 70 students, find the mean and standard deviation for the numb

ID: 3124920 • Letter: A

Question

a. For classes of 70 students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.

b. For a class of 70 students, would two be an unusually high number who were born on the 4th of July?

a. The value of the mean is = ____. (Round to six decimal places as needed.)

The value of the standard deviation is = _____. (Round to six decimal places as needed.)

b. Would 2 be an unusually high number of individuals who were born on the 4th of July?

A. No comma because 2 is within the range of usual values.No, because 2 is within the range of usual values.

B. Yes comma because 2 is greater than the maximum usual value.Yes, because 2 is greater than the maximum usual value.

C. Yes comma because 2 is below the minimum usual value.Yes, because 2 is below the minimum usual value.

D. This result is unlikely because 2 is within the range of usual values.

The probability of being born on July 4 is p = 1/365 = 0.002739726.

As n = 70, and

u = n p

Then

u = 70*0.002739726 = 0.191781 [ANSWER]

Also,

sigma = sqrt(np(1-p)) = sqrt(70*0.002739726*(1-0.002739726)) = 0.437328 [ANSWER]

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b. Would 2 be an unusually high number of individuals who were born on the 4th of July?

2 is unusual if its z score is greater than 2.

z = (x-u)/sigma

Then for x = 2,

z = (2-0.191781)/0.437328 = 4.13469

As z > 2, then

OPTION B. Yes, because 2 is greater than the maximum usual value. [ANSWER]

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