A population of values has a normal distribution with μ=208.5μ=208.5 and σ=94.8σ=94.8. You intend to draw a random sample of size n=85n=85.

Question

A population of values has a normal distribution with μ=208.5μ=208.5 and σ=94.8σ=94.8. You intend to draw a random sample of size n=85n=85. Please show your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is between 178.7 and 198.2. 

P(178.7 < X < 198.2) =  

Find the probability that a sample of size n=85n=85 is randomly selected with a mean between 178.7 and 198.2. 

P(178.7 < ¯xx¯ < 198.2) =  

Answer 1

probability that a single randomly selected value is between 178.7 and 198.2. 

P(178.7 < X < 198.2)

= normalcdf (178.7, 198.2, 208.5, 94.8)

= 0.0801

probability that a sample of size n=85n=85 is randomly selected with a mean between 178.7 and 198.2. 

P(178.7 < ¯X¯ < 198.2)

= normalcdf (178.7, 198.2, 208.5, 94.8/√85)  

= 0.1564