Question

Check my ork A normal population has a mean of 58 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean Is: (Round your z values to 2 declmal places and final answers to 4 deeclmal places): 12 polnts a. Greater than 60. eBook Ask Print References b. Less than 57 Probability

Answer 1

Answer:

We know that Z score is given by,

uN2 =Z Η – X

Where $\bar{X}$ is the sample mean

$\mu$ is the population mean

$\sigma$ is the population standard deviation and n is sample size.

(a) Given,
u=58
,
0 = 13
, and n=25

Thus the probability that the sample mean is great than 60, i.e.

X = 60

We get,

Z-X - 60 - 58 gVn 13/V25

And from Z table we get that the probability of is 0.7791.

Z = 0.769

(b) When sample mean is less than 57:

Z-X-H 0/n 57 - 58 137. = -0.385

And from Z table we get that the probability of is 0.3503.

Z= -0,385

(c) When sample mean between 57 and 60:

From the above calculation, and

P(X>60) = 0.7791(for Z = 0.769)

P(X <57) = 0.3503 for Z = -0.385)

Thus,

P(57 < X < 60) = P(X>60) - P(X<57) = 0.7791 -0.3503 = 0.4289