The Average Lifetime of a Light Bulb Is 3,000 Hours

question 43

Essay

The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken.
a.What are the expected value, standard deviation, and shape of the sampling distribution of?
b.What is the random variable in this problem? Define it in words.
c.What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours?
d.What is the probability that the average life in the sample will be greater than 3,219.24 hours?
e.What is the probability that the average life in the sample will be less than 3,180.96 hours?

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Definitions:

Cloak of Competence

A term describing situations where an individual with cognitive or developmental disabilities appears to function at a higher level than actually is the case, masking potential deficits.

Developmental Disorders

A group of psychiatric conditions originating in childhood that involve serious impairment in different areas, such as cognitive and physical development.

Pass as "Normal"

The attempt of an individual to be perceived as adhering to societal norms, especially when their inherent traits or conditions deviate from these norms.

Phenylketonuria (PKU)

A genetic disorder characterized by the body's inability to metabolize the amino acid phenylalanine, leading to intellectual disability if not treated early.