Question

A random sample of size 49 is taken from a population with mean µ = 26 and standard deviation σ = 7. Use an appropriate normal transformation to calculate the probability that the sample mean is between 24 and 27.

Group of answer choices

0.0228

0.8641

0.8413

0.8185

Answer 1

Solution :

Given that,

mean = = 26

standard deviation = = 7

= / n = 7/ 49 = 1

= P[(24 - 26) / 1< ( - ) / < (27 - 26) / 1)]

= P(-2 < Z < 1)

= P(Z < 1) - P(Z < -2)

= 0.8413 - 0.0228

= 0.8185

Probability = 0.8185