A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P (

Question

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find P (  < 48).

Quizplus · Accepted Answer

To solve this problem, we need to standardize the random variable using the standard normal distribution.

First, find the standard error of the mean (SEM):

SEM = σ / sqrt(n)
SEM = 5 / sqrt(36)
SEM = 5 / 6 = 0.8333

Next, standardize the random variable x:

z = (x - μ) / SEM
z = (48 - 50) / 0.8333
z = -2.4

Finally, find the probability using a standard normal distribution table or calculator:

P(z < -2.4) = 0.0082

Thus, the answer is A) .0082.

A Random Sample of Size 36 Is Taken from a Population