A population of values has a normal distribution with =155.5=155.5 and =58.3=58.

Question

A population of values has a normal distribution with =155.5=155.5 and =58.3=58.3. You intend to draw a random sample of size n=221n=221.

Find the probability that a single randomly selected value is greater than 148.8.
P(X > 148.8) =

Find the probability that a sample of size n=221n=221 is randomly selected with a mean greater than 148.8.
P(M > 148.8) =

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.

Explanation / Answer

1) probability that a single randomly selected value is greater than 148.8 =P(X>148.8)

=P(Z>(148.8-155.5)/58.3)=P(Z>-0.1149)=0.5457

2)

std error of mean =std deviation/(n)1/2 =58.3/(221)1/2 =3.9217

probability that a sample of size n=221 is randomly selected with a mean greater than 148.8

=P(Xbar>148.8) =P(Z>(148.8-155.5)/3.9217)=P(Z>-1.7085)=0.9562

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