Statistics and Probability Answers

The mean expenditure per customer at a department store is Birr 85 with standard deviation of Birr 9. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer will be
a) Birr 87 or more
b) Less than Birr 82
c) Between Birr 83 and 85

The mean expenditure per customer at a department store is Birr 85 with standard deviation of Birr 9. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer will be
a) Birr 87 or more
b) Less than Birr 82
c) Between Birr 83 and 85

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of
the paint

It is claimed that automobiles are driven on average more than 20,000 kilometers per year. To test this claim, 100 randomly selected automobile owners are asked to keep a record of the kilometers they travel. Would you agree with this claim if the random sample showed an average of 23,500 kilometers and a standard deviation of 3900 kilometers?

A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. The final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A , what is the probability that he or she is a senior?

The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that
(i) a married couple watches the show;
(ii) a wife watches the show, given that her husband does;
(iii) at least one member of a married couple will watch the show.

What is the probability that a random sample of 70 pregnancies has a mean gestation period of 124 days or​ less?

1. Bags of smokeless fuel are labeled as weighing 100kg, but actual weights are normally distributed with a mean of 102kg and a standard deviation of 4kg.
(i) What proportion of bags will weigh more than 106kg? ii) What proportion of bags will weigh less than 95kg?
(iii) What proportion of bags will weigh between 91kg and 112kg?

A computer manager needs to know how efficiency of her new computer program depends
on the size of incoming data. Efficiency will be measured by the number of processed
requests per hour. Applying the program to data sets of different sizes, she obtains the
following results,
Data size (gigabytes) 6 7 7 8 10 10 15
Processed requests 40 55 50 41 17 26 16
i. Draw the scatterplot for the data. Be sure to label your axes.
ii. Is there any correlation between the processing request and the size of incoming data?
What is the correlation coefficient?
iii. By what percentage is the processing time dependent on the size of incoming data?
iv. Compute a least square regression line for regressing processing request on the size of
incoming data.
v. Use your regression equation to predict the processing request for an incoming data
of size 17.0 gigabytes
vi. Is the slope statistically significant at α = 5% ?

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41%
of college students nationwide engage in binge drinking behavior, having 5 or more drinks in one occasion during the past two
weeks. In a commissioned study, 462 students are selected randomly from a list of all students enrolled at the college. Of these,
162 admitted to having engaged in binge drinking. Based on the results of the study, find a 98% confidence interval for the
proportion of all students at this college that engage in binge drinking