Question

The measured glucose level one hour after having a sugary drink varies according to the normal distribution with μ = 112 mg/dl and ϭ = 20 mg/dl.

a) What is the level (call it L) such that there is probability of only 0.01 that the sample mean glucose level from five tests falls above L? (Hint: this is a Normal Table problem)

b) If a sample of 5 glucose tests actually had a mean of 120 mg, what is the probability of getting a sample mean greater than 120 mg?

Answer 1

Mean = = 112

Standard deviation = = 20

a) We have given P(X > L) = 0.01

Z value is 2.32 ( Using z table)

b)

Sample size = n = 5

We have to find P( > 120)

For finding this probability we have to find z score.

That is we have to find P(Z > 0.89)

P(Z > 0.89) = 1 - P(Z < 0.89) = 1 - 0.8133 = 0.1867