Probability, Test Statistics and Error

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 meanof 37.9 and a standard deviationof 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 probabilityof 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 ___________

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*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 sampleof 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 intervalto 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 ________

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*Construct the 95% and 99% confidence intervalsfor the population proportion “p” using the sample statisticsbelow. 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 binomialdistribution 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 distributionis 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)

The following helps calculate problems involving critical value, substantiatzed