A Sample of 50 Observations Is Drawn at Random from a Normal

question 31

Essay

A sample of 50 observations is drawn at random from a normal population whose mean and standard deviation are 75 and 6, respectively.
a. What does the central limit theorem say about the sampling distribution of the sample mean? Why?
b. Find the mean and standard error of the sampling distribution of the sample mean.
c. Find P( $\bar { X }$ > 73).
d. Find P( $\bar { X }$ < 74).

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Definitions:

Higher Conscientiousness

Exhibiting an increased level of the trait characterized by organization, dependability, and carefulness.

Social Investment Theory

A psychological theory suggesting that as individuals mature, they invest more in their social roles, which leads to an increase in conscientiousness and stability.

Longevity

The duration of an individual's life, often used in discussions about factors that contribute to a long and healthy life.

Personality Maturation

The process of growth and development in one's personality traits, often leading to increased stability and decreased neuroticism over time.