Question

A population of values has a normal distribution with μ=5.8μ=5.8 and σ=17σ=17. You intend to draw a random sample of size n=225n=225.

Find the probability that a single randomly selected value is less than 9.
P(X < 9) =

Find the probability that a sample of size n=225n=225 is randomly selected with a mean less than 9.

P(M < 9) =

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

This is a normal distribution question with

P(x < 9.0)=?
The z-score at x = 9.0 is,

z = 0.1882
This implies that


This is a normal distribution question with

Sample size (n) = 225
Since we know that

P(x < 9.0)=?
The z-score at M = 9.0 is,

z = 2.8236
This implies that

PS: you have to refer z score table to find the final probabilities.
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