Question

1. A population with a normal distribution has a mean of 104 and standard deviation 15. A sample of 30 items is taken from that population. (a) (4 points) What is the probability of the sample mean being not less than 103?

Answer 1

Answer:

0.3575

Step-by-step explanation:

A population with a normal distribution has a mean of 104 and a standard deviation of 15. A sample of 30 items is taken from that population. (a) (4 points) What is the probability of the sample mean is not less than 103?

The probability of the sample mean is not less than 103 means the sample mean is equal to 103

We solve using the z score formula

z = (x-μ)/σ/√n

where

x is the raw score = 103

μ is the population mean = 104

σ is the population standard deviation = 15

n is the random number of sample = 30

z = 103 - 104/15/√30

z = -1/2.7386127875

z = -0.36515

Probability value from Z-Table:

P(x≤ 103) = 0.3575

Therefore, the probability of the sample mean is not less than 103 is 0.3575