Question

A population of values has a normal distribution with μ=38.4 and σ=67.7. You intend to draw a random sample of size n=20.

Find the probability that a single randomly selected value is less than -10.
P(X < -10) = ..........................

Find the probability that a sample of size n=20 is randomly selected with a mean less than -10.
P(M < -10) = ............................

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

Answer:

Given that,

A population of values has a normal distribution with μ=38.4 and σ=67.7. You intend to draw a random sample of size n=20.

i.e,

μ=38.4

σ=67.7

n=20

(a).

Find the probability that a single randomly selected value is less than -10.
P(X < -10):

=38.4

=67.7/4.472

=15.1386

=P[Z < -3.1971]

=1-P[Z < -3.1971]

=1-0.9993

=0.0007

=0.001 (Approximately)

Therefore, the probability that a single randomly selected value is less than -10.
P(X < -10)=0.001.

(b).

Find the probability that a sample of size n=20 is randomly selected with a mean less than -10.

P(M < -10):

=38.4

=67.7/4.472

=15.1386

=P[Z < -3.1971]

=1-P[Z < -3.1971]

=1-0.9993

=0.0007

=0.001 (Approximately)

Therefore, the probability that a single randomly selected value is less than -10.
P(M < -10)=0.001.