The population of weights for men attending a local health club is normally distributed with a mean of 180-lbs and a standard deviation of 25-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 6112-lbs.

Assume that there are 32 men in the elevator. What is the average weight of the 32 men beyond which the elevator would be considered overloaded?
average weight = _________ lbs

What is the probability that one randomly selected male health club member will exceed this weight?
P(one man exceeds) = _____________
(Report answer accurate to 4 decimal places.)

If we assume that 32 male occupants in the elevator are the result of a random selection, find the probability that the elevator will be overloaded?
P(elevator overloaded) =____________
(Report answer accurate to 4 decimal places.)

If the elevator is full (on average) 6 times a day, how many times will the elevator be overloaded in one (non-leap) year?
number of times overloaded = _________________
(Report answer rounded to the nearest whole number.)

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 167000 dollars. Assume the standard deviation is 32000 dollars. Suppose you take a simple random sample of 100 graduates.

Find the probability that a single randomly selected salary is more than 162000 dollars.
P(X > 162000) = _______

Find the probability that a sample of size n=100 is randomly selected with a mean that is more than 162000 dollars.
P(M > 162000) = _________

Enter your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with μ=124.2 and σ=75.5. You intend to draw a random sample of size n=35

Find the probability that a single randomly selected value is between 121.6 and 145.9.
P(121.6 < X < 145.9) = ____________

Find the probability that a sample of size n=35 is randomly selected with a mean between 121.6 and 145.9.
P(121.6 < M < 145.9) = __________

Enter your answers as numbers accurate to 4 decimal places.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.893 g and a standard deviation of 0.306 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 44 cigarettes with a mean nicotine amount of 0.819 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 44 cigarettes with a mean of 0.819 g or less.
P(M < 0.819 g) = _________
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

A population of values has a normal distribution with μ=172.6 and σ=36. You intend to draw a random sample of size n=192

Find P₈₂, which is the score separating the bottom 82% scores from the top 18% scores.
P₈₂ (for single values) = ____________

Find P₈₂, which is the mean separating the bottom 82% means from the top 18% means.
P₈₂ (for sample means) = ___________

Enter your answers as numbers accurate to 1 decimal place.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 93.6-cm and a standard deviation of 1.6-cm. For shipment, 30 steel rods are bundled together.

Find P₃₂, which is the average length separating the smallest 32% bundles from the largest 68% bundles.
P₃₂ =___________ -cm

Enter your answer as a number accurate to 2 decimal place.

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.1 years, and standard deviation of 1.1 years.

If 19 items are picked at random, 10% of the time their mean life will be less than how many years?

Give your answer to one decimal place._________________

A sample sequence of 35 products is selected (in order) from an assembly line. Each product is examined and judged to be either acceptable or defective. A total of 26 of these products were found to be acceptable, and the other 9 were found to be defective. The number of runs was 7. The runs test is to be used at the 0.05 significance level to test for randomness. Find the value of the test statistic used in this test, and round it to 3 places after the decimal point (if necessary)

What is the least squares method and how is it used to find the estimated regression equation? What is the role of least squares method in calculating coefficient of determination? Explain.

A random sample of 100100 observations produced a mean of x¯¯¯=38.6x¯=38.6 from a population with a normal distribution and a standard deviation σ=4.42σ=4.42.

(a) Find a 9090% confidence interval for μμ
≤μ≤≤μ≤

(b) Find a 9595% confidence interval for μμ
≤μ≤≤μ≤

(c) Find a 9999% confidence interval for μμ
≤μ≤≤μ≤

Government regulations restrict the amount of pollutants that can be released into the atmosphere through industrial smokestacks. REM industries claims that their smokestacks release an average number of pollutants of 5 parts per billion. To test this claim, the government collects a sample from 81 smokestacks and finds that the mean pollutant level is 4.79 parts per billion. Suppose the standard deviation is known to be 1.08 parts per billion. Is there enough evicence to suggest that the average number of pollutants is different from the claim at the .05 level of significance? Use the p-value approach to make your decision.

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups: group 1 takes the drug, group 2 takes a placebo. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 20 participants on the drug had an average test score of 24.62 (SD = 4.649) while those 27 participants not on the drug (taking the placebo) had an average score of 28.85 (SD = 6.365). You use this information to perform a test for two independent samples with hypotheses Null Hypothesis: μ₁ ≥ μ₂, Alternative Hypothesis: μ₁ < μ₂. What is the test statistic and p-value? Assume the population standard deviations are equal.

Question 3 options:

A researcher wanted to know whether people drive faster in sports cars or pick up trucks. He went out on the freeway with a radar gun and track the speed of people in both types of cars. A sample of n=30 sport car drivers went an average of M=69 (s=5.35) whereas a sample n=30 pick up truck drivers wet an average of M=67 9 (s=5.30). What statistics should be run? Calculate Harlteys F-Max, one-tailed to two-tailed test, calculate confidence interval of 95%, calculate appropriate statistic

Research into the relationship between hours of study and grades shows widely different conclusions. A recent survey of graduates who wrote the Graduate Management Admissions Test (GMAT) had the following results.       

Hours

Studied            Average

(Midpoint)      Score

40                    210

50                    300

65                    345

75                    455

85                    540

105                  660

95                    700

1. Run the regression analysis in Excel on this data. Include your output with your answer. (Note: You may calculate by hand if you prefer).
2. What is the regression equation for this relationship?
3. Use the regression equation to predict the average score for each category of hours studied.
4. Plot the original data and the regression line on a scattergram. (You may use Excel).
5. How accurate is this regression at predicting GMAT scores based on hours studied? Explain.
6. Use the t statistic to determine whether the Correlation Coefficient is “significant” at the 95% confidence level.