# Probability, Test Statistics and Error

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In a recent year, scores on a standardized test for high schools student with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 37.9 and a standard deviation of 2.4. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected.

Four Decimal Places for Questions

Find the probability of a student test score less than 36

The probability of a student scoring less than 36 is ________

Find the probability of a student test score between 35.1 and 40.7

The probability of a student scoring between 35.1 and 40.7 is ________

Find the probability of a student test score more than 39.3

The probability of a student scoring more than 39.3 is ___________

_________________________________

*A microwave oven repairer says that the mean repair cost for damaged microwave ovens is less than $110. You work for the repairer and want to test this claim. You find that a random sample of five microwave ovens has a mean repair cost of $115 and a standard deviation of $12.50. At a=0.05, do you have enough to support the repairer's claim? Assume the population is normally distributed.

What is (are) the critical value(s), t0? t0 = _________

Find the standardized test statistic t = __________

*Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of (2,9,4,5) when estimating the mean height (in centimeters) of a sample seedlings.

A. The estimated margin of error is _______

B. The Sample mean is ________

_____________________________________________

*Construct the 95% and 99% confidence intervals for the population proportion "p" using the sample statistics below. Which interval is wider? If convenient, use technology to construct the confidence intervals.

Three decimal places as needed

95% confidence intervals for the population proportion "p" is _____ - ______

99% confidence intervals for the population proportion "p" is _____ - ______

Which interval is wider? 95% confidence intervals or 99% confidence intervals

__________________________________________

*Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p: n=80, p=0.5

The mean, u, is __________ (nearest tenth)

Variance, 2 is_______ (nearest tenth)

The standard deviation, , is ________ (nearest tenth)

______________________________________________

*A frequency distribution is shown below. Complete part (a) through (e)

The number of dogs per household in a small town

Dog 0 1 2 3 4 5

Household 1370 406 163 50 26 16

0 ___ 1___2___3___4___5___ (nearest thousand)

Find the mean of the probability distribution: u=______ (nearest tenth)

Find the variance of the probability distribution: 2 = ________(nearest tenth)

Find the standard deviation of the probability distribution: = ___(nearest tenth)

#### Solution Summary

The following helps calculate problems involving critical value, substantiatzed