Question

Normal Distribution CI

IQ tests are designed to yield results that are approximately Normally distributed. Researchers think believe that the standard deviation, σ, is 15. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22 employees of this firm and recoreds the sample mean IQ as 106. Let X represent a random variable describing a person's IQ: X~N(µ, 15).

a. Find the standard error of the sample mean.

b. Calculate a 90% confidence interval.

c. Interpret the confidence interval in the context of the
problem.

Answer #1

It is assumed that individual IQ scores (denoted as X) are
normally distributed with mean (µ) and standard deviation (σ) given
as µ = 100 and σ = 15 Use normal table and conversion rule to
answer questions below.
1. Find proportion of individuals with IQ score below 109
2. Find a chance that a randomly selected respondent has the IQ
score above 103
3. What proportion of individuals would be within the interval
(97 ≤ X ≤ 106)
4....

Recall in our discussion of the normal distribution the research
study that examined the blood vitamin D levels of the entire US
population of landscape gardeners. The intent of this large-scale
and comprehensive study was to characterize fully this population
of landscapers as normally distributed with a corresponding
population mean and standard deviation, which were determined from
the data collection of the entire population.
Suppose you are now in a different reality in which this study
never took place though...

Recall in our discussion of the normal distribution the research
study that examined the blood vitamin D levels of the entire US
population of landscape gardeners. The intent of this large-scale
and comprehensive study was to characterize fully this population
of landscapers as normally distributed with a corresponding
population mean and standard deviation, which were determined from
the data collection of the entire population.
Suppose you are now in a different reality in which this study
never took place though...

Recall in our discussion of the normal distribution the research
study that examined the blood vitamin D levels of the entire US
population of landscape gardeners. The intent of this large-scale
and comprehensive study was to characterize fully this population
of landscapers as normally distributed with a corresponding
population mean and standard deviation, which were determined from
the data collection of the entire population. Suppose you are now
in a different reality in which this study never took place though...

PLEASE SHOW ALL WORKING STEPS. THANKS
8. Recall in our discussion of the normal distribution the
research study that examined the blood vitamin D levels of the
entire US population of landscape gardeners. The intent of this
large-scale and comprehensive study was to characterize fully this
population of landscapers as normally distributed with a
corresponding population mean and standard deviation, which were
determined from the data collection of the entire population.
Suppose you are now in a different reality in...

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