STAT 050 PCC Normal Probability Distribution and Estimating Parameters Questions

Question Description

7 questions like

1. If z is a standard normal variable, find the probability that z lies between 1.25 and 2.45.

2. A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 25 mechanics are randomly selected, find the probability that their mean rebuild time is less than 9 hours.

3. Membership in Mensa requires a score in the top 2% on a standard intelligent test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed.

a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement

b. If 4 randomly selected adults take the Wechsler IQ test, find the probability that their mean score is at least 131.

c. If 4 subjects take the Wechsler test and they have a mean of 132 but the individual scores are lost, can we conclude that all 4 of them are eligible for Mensa?

4. An economist wants to know if the proportion of the children in the United States that speak a language other than English at home has changed since 2016, when 22% of children did. How many children would need to be surveyed if the economist wants to be within 2 percentage points of the true proportion with 92% confidence?

5. Of 254 randomly selected medical students, 25 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.

6. When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.

a. Find a 99% confidence interval estimate of the percentage of yellow peas.

b. Based on his theory of genetics, Mandel expected that 25% of the offspring peas would be yellow. Given that percentage of offspring yellow peas is not 25%, do the results contradict Mendel’s theory? Why or why not?

7. Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. n = 30, x = 84.6, s = 10.5, 90% confidence level. Hints: determine if the is known.

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