Question

A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475. A. 0.3251 B. 0.0712 C. 0.7124 D. 0.0475

Answer 1

Answer:

D

Step-by-step explanation:

We start out by calculating the z-score

z = (x-mean)/SD/√n

x = 475

mean = 500

SD = 60

n = 16

Substituting these;

z = (475-500)/60/√16

z = (-25)/60/4

z = -25/15

z = -1.67

So the probability we want to

calculate is P (x < -1.67)

we can use the standard normal distribution table here;

And from the standard normal distribution table;

we have P( x < -1.67) as 0.04746

which is approximately 0.0475

Answer 2

The probability that this population will have a sample mean less than 475 is 0.0475

z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ \mu=mean,\sigma=standard\ deviation,x=raw\ score,n=sample\ size$

Given that n = 16, μ = 500, σ = 60.

For x < 475:

$z=\frac{475-500}{60/\sqrt{16} } =-1.67$

From the normal distribution table, P(x < 475) = P(z < -1.67) = 0.0475

The probability that this population will have a sample mean less than 475 is 0.0475

Find out more on z score at: https://brainly.com/question/25638875