Question

A simple random sample of 100 men is chosen form a population with mean height 71 in and standard deviation 2.5 in. What is the probability that the average height of the men in the sample is less than 70.5in?

Answer 1

2.28%

Explanation:

The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:

`z=(x-\mu)/(\sigma)\\ \\\mu = mean, \sigma=standard\ deviation,x=raw\ score\\\\For\ a\ sample\ n\\\\z=(x-\mu)/(\sigma/√(n) )\\\\For\ x<70.5\ in\\\\Given \ that\ n=100, \mu=71\ in, \sigma=2.5\ in\\\\z=(70.5-71)/(2.5/√(100) )=-2\\\\From\ normal\ distribution\ table, P(x<70.5)=P(z<-2)=0.0228=2.28\%`