Suppose a Random Sample of 25 Students Is Selected from a Community

question 103

Short Answer

Suppose a random sample of 25 students is selected from a community college where the scores in the final exam (out of 125 points) are normally distributed, with mean equal to 112 and standard deviation equal to 12.
What is the mean of the sampling distribution of the sample mean ?
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What is the standard deviation?
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Find the probability that exceeds 116.
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Find the probability that the sample mean deviates from the population mean = 112 by no more than 4.
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Definitions:

Rollo May

Rollo May was an American psychologist and one of the founders of existential psychology, emphasizing the importance of anxiety and the human condition.

Humanistic Theory

Humanistic theory emphasizes individual potential, self-growth, and the importance of meeting psychological needs for love, esteem, and self-actualization.

Positive Regard

The acceptance, respect, and appreciation that one person shows another, considered essential in humanistic psychology for healthy personal development.

Psychodynamic Theorists

Researchers and clinicians who explore how unconscious processes and childhood experiences affect personality and behavior.