Please help with statistics

Question

A population of values has a normal distribution with  and . You intend to draw a random sample of size .

Find the probability that a single randomly selected value is between 148.3 and 159.5.P(148.3 < X < 159.5)

Find the probability that a sample of size  is randomly selected with a mean between 148.3 and 159.5.P(148.3 < M < 159.5)

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

p (148.3 < X < 159.5)

On a TI-84 :

normalcdf

lower = 148.3

upper = 159.5

mean = 156.9

sd = 92.2

p (148.3 < M < 159.5)

mean is distributed normally, with mean = 156.9 , sd = 92.2 / √195

use the normalcdf