Question

Assume the random variable x is a normal distribution with the mean=81 and the standard deviation sigma =5

Answer 1

Assume the random variable x is a normal distribution with the mean=81 and the standard deviation sigma =5​

P(x<77)

step 1

Find out the z-score

we have that

Z score =(x - μ)/σ

is given

x=77

μ=81

σ=5

substitute

Z-score=(77-81)/5

Z-score=-0.8

using a z-score probability calculator or tables

Probability of x<77:

P=0.2119