SOLUTION: 1.The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9. A sample of the numbers of people in line in 50 stores is taken - Ca

Algebra ->  Probability-and-statistics -> SOLUTION: 1.The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9. A sample of the numbers of people in line in 50 stores is taken - Ca      Log On


   

Question 1176779: 1.The distribution of the number of people in line at a grocery store has a mean of 3 and a variance of 9.
A sample of the numbers of people in line in 50 stores is taken - Calculate the probability that the sample mean is more than 4. - Calculate the probability the sample mean is less than 2.5. - Calculate the probability that the sample mean differs from the population mean by less than 0.5.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Normal distribution:  mean of 3, a variance of 9  and σ = 3
Sample:  n = 50
  z+=blue+%28x+-+mu%29%2Fblue%28sigma%2Fsqrt%28n%29%29  3/sqrt(50) = .4242640687

 P( x̄ > 4) = 1 - P( x̄ ≤  4)  0r 1 - P(z ≤ 1/(3/sqrt(50)) = 1-.6306

 P( x̄ < 2.5) = P( x̄ ≤ 2.5)  0r P(z ≤ -.5/(3/sqrt(50)) = .4338

 P( x̄ < .5) = P( x̄ ≤ .5)  0r P(z ≤ -2.5/(3/sqrt(50)) = .2023

Wish You the Best in your Studies.