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:

Visual Cliff

A psychological experiment designed to study the perception of depth and the development of fear of falling in infants.

Perceptual Development

The gradual improvement in the ability to process and interpret sensory information through the senses as one grows from infancy through childhood.

Motor Development

The progression of muscle coordination, strength, and the ability to move and control body movements, crucial in childhood for acquiring skills like crawling, walking, and grasping.

Anesthesia

A medical treatment that involves the use of drugs to prevent pain during surgery, resulting in loss of sensation or consciousness.