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# Category Archives: Normal Distribution

## Null Hypothesis Test for MEAN example question

A literary critic wants to establish that the mean number of words per sentence, appearing in newly discovered short story is different from 9.1 words. A sample of 36 sentences provided a data with mean of 8.6 words and standard deviation of 1.2 words. Test at a level of significance α = 0.10.

Solution to this Hypothesis Testing Statistics practice problem is given in the video below!

## Null Hypothesis Test for PROPORTION example problem

Out of a sample of n = 625 students interviewed, 139 missed at least one class last week. Let p = proportion of students that missed at least one class last week. Conduct a test with the intent of establishing that the proportion of students that missed at least one class last week is greater than 0.20. Test at a level of significance α = 0.05.

Solution to this Hypothesis Testing Statistics practice problem is given in the video below!

## Confidence Interval for MEAN Normal Distribution example question

A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a 90% confidence interval for the mean time to process μ.

Solution to this Confidence Interval Statistics practice problem is given in the video below!

## T-Distribution Confidence Interval for MEAN example

From a random sample of size 16, one has calculated the 95% confidence interval for μ (population mean) and obtained the result (39.51, 42.49). What are the (sample mean) and s (sample standard deviation) for the sample? Assume the population is normal.

Solution to this Confidence Interval Statistics practice problem is given in the video below!

## Confidence Interval for PROPORTION Normal Distribution example problem

A telephone survey of 1,000 was taken after movie X came out in the national theater.

a) If 832 liked the movie, with what confidence can it be asserted that 83.2% ± 3% of the adult population liked this movie?

b) If the adult population in the nation is 150 million, what is the interval estimating the total number of people in the nation who liked the movie?

Solution to this Confidence Interval Statistics practice problem is given in the video below!

## Normal Distribution Probability example question

The annual rainfall (in inches) in a certain region is normally distributed with = 40,  = 4. What is the probability that starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches?

Solution to this Normal Continuous Random Variable Distribution Probability practice problem is given in the video below!

## Normal Distribution PERCENTILE Probability example problem

The measure of intelligence of a group of people is assumed to be approximately normally distributed with mean 102 and standard deviation 14. If we are told that Tom’s IQ denoted by xT is at the 98th percentile of the IQ distribution of the group of people, find xT.

Solution to this Normal Continuous Random Variable Distribution Probability practice problem is given in the video below!