1.) A population of values has a normal distribution with=23.5and=42.7.You intend to draw a random sample of size n=37.Please show your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is less than 26.3.

P(X< 26.3) =

Find the probability that a sample of sizen=37n=37is randomly selected with a mean less than 26.3.

P(X< 26.3) =

2.)A population of values has an unknown distribution with=224.5and =97.7. You intend to draw a random sample of sizen=131.

What is the mean of the distribution of sample means?

_x=(Please enter an exact answer.)

What is the standard deviation of the distribution of sample means?

^x=(Please report your answer accurate to 2 decimal places.)

3.) A population of values has a normal distribution with=106 and=13.9. You intend to draw a random sample of sizen=27.

Find the probability that a single randomly selected value is less than 103.1.

P(X< 103.1) =

Find the probability that a sample of sizen=27 is randomly selected with a mean less than 103.1.

P(M< 103.1) =Enter your answers as numbers accurate to 4 decimal places.

4.)A population of values has a normal distribution with=135 and=93.4. You intend to draw a random sample of sizen=35.Please show your answers as numbers accurate to 4 decimal places.

Find the probability that a single randomly selected value is between 116.1 and 168.2.

P(116.1 <X< 168.2) =

Find the probability that a sample of sizen=35 is randomly selected with a mean between 116.1 and 168.2.

P(116.1