Probability Statistics - URGENT

Question

A population is normally distributed with mean 17.9, and a standard deviation of 3.5. fine the probability that a sample of 14 values take from the population will have a mean less than 16.

* all z scores must be rounded to the nearest hundredth

Answer 1

Hello,

The first thing that would be best for you to do is calculate the sample standard deviation from the population standard deviation provided. The formula for this is sample standard deviation = population standard deviation / square root of sample size (s=3.5/sqrt(14)).

The next step is to calculate the z-score. The formula is z-score = (observed value - mean) / sample standard deviation (z=(16-17.9) / (3.5/sqrt(14))). The z-score you end up getting is -2.031. If you look up the corresponding value on the z-table, the answer is 0.0212.