Question

Over the entire six years that students attend an ohio elementary school, they are absent, on average, 28 days due to influenza. assume that the standard deviation over this time period is σ = 9 days. upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. the probability that the sample mean is less than 30 school days is _______.

Answer 1

The probability that the sample mean is less than 30 school days will be given as follows:
the z-score is given by:
z=(x-μ)/σ
where
μ- stand deviation
σ-mean
thus the z-score of our information is:
z=(30-28)/9
z=0.222222
hence the probability that the sample mean is less than 30 will be:
P(x<30)=0.5871~58.71%