Question

In: Statistics and Probability

Consider a large population of interest. It's distribution is normal and it's mean is 187 and...

Consider a large population of interest. It's distribution is normal and it's mean is 187 and standard deviation is 112. Let X = a single observation.

(Round all probabilities to four decimals)

a) Find P(X < 192):

A random sample of 126 is taken. Let X¯ = sample average of the observations.

b) Find P( X¯ < 192):

Consider another large population of interest. It's distribution is unknown and it's mean is 187 and it standard deviation is 112. Let Y = a single observation.

A random sample of 126 is taken. Let Y¯ = sample average of the observations.

c) Find P( Y¯ < 192):

Expert Solution

Given: The distribution of X is normal and it's mean is 187 and standard deviation is 112.

a) The required probability is:

## By using z table.

A random sample of 126 is taken. Let X¯ = sample average of the observations.

b)

## By using z table.

Consider another large population of interest. It's distribution is unknown and it's mean is 187 and it standard deviation is 112. Let Y = a single observation.

A random sample of 126 is taken. Let Y¯ = sample average of the observations.

c)

### Since the sample size is large the sampling distribution of sample mean is normal according to the central limit theorem.

### By using z table.

orchestra answered 2 years ago

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