Question

A population of values has a normal distribution with μ=50 and σ=98.2. You intend to draw a random sample of size n=13.

Find the probability that a single randomly selected value is less than -1.7. P(X < -1.7) =

Find the probability that a sample of size n=13 is randomly selected with a mean less than -1.7.
P(M < -1.7) =

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

The given information is,

(1). The probability that a single randomly selected value is less than -1.7 is obtained by using the z-table as,

Therefore, the probability that a single randomly selected value is less than -1.7 is 0.2981.

(2).

The probability that a sample of size n=13 is randomly selected with a mean less than -1.7 is obtained by using the z-table as,

Therefore, the probability that a sample of size n=13 is randomly selected with a mean less than -1.7 is 0.0287.