In a class there are 60 students. The mean exam score is 70 and the
standard deviation is 5. (Be Precise in your answers!) Assume symmetric
distribution of the scores.

(i) What can you say about the number of students that have scores between
55 and 85?

(ii) What can you say about the number of students who have scores between
60 and 80?

4) Let Z have a standard normal distribution. Find the following
probabilities:
a) P(Z is between -2.52 and 2.67)

b) P( Z is more than -1.26)

5) A gas company president for a particular city is interested in the
proportion of homes heated by gas. Historically, the proportion of homes
heated by gas has been 65%. A sample of 75 home was selected and it was
found that 44 of them heat with gas. Perform the appropriate test of
hypothesis to determine whether the proportion of home heated by gas has
changed. Test using the 5% level of significance.

6) A class had a mean of 67 in the final exam and a standard deviation of
5. The class has more poorly performing students than those who perform
well. What can you say about the percentage of students who have scores
between 57 and 77?

7) Tough Road Tire Company wants to test its new brand of tires. The
engineering department of the company claims that the new tires last more
than 40,000 miles in the average. A sample of 40 tires was tested and found
that the average number of miles they lasted for the sample was 43,200 miles
with a standard deviation of 8000 miles. At the level of significance 0.05,
can the company claim that the tires last an average of more than 40,000
miles? Show all your work.

8) A weight loss program measured the weights lost by 12 participants. For
this sample of 12 participants the mean weights lost was 15.2 pounds and the
standard deviation was 5.3 pounds. Find the 95% confidence interval for the
average ( mean ) weight lost by the participants of this program. Assume
that the weights lost by the participants follow a normal distribution.

Solution Summary

The solution provides step by step method for the calculation of normal probability and confidence intervals . Formula for the calculation and Interpretations of the results are also included.

In a random sample of 62 bolts, the mean length was 1.87 inches and the standard deviation was 0.07 inch. Use a normal distribution or a t-distribution to construct a 90% confidenceinterval or the mean.
Which distribution should be used to construct the 90% confidenceinterval?
A. Use a normal distribution because the len

1. What do confidenceintervals represent? What is the most controllable method of increasing the precision (narrowing) of the confidenceinterval? What percentage of times will the mean (population proportion) not be found within the confidenceinterval?
2. As a sample size approaches infinity, how does the t distribution co

The body mass index (BMI) for a sample of men and a sample of women are given below. Assume the samples are simple random samples obtained from populations with normaldistributions.
[Please refer to the attachment for the data].
Construct an 80% confidenceinterval estimate of the standard deviation of BMIs for men.

Which of the following is not needed to be known to calculate a confidenceinterval?
a. standard deviation
b. sample size
c. mean
d. degree of confidence

If x bar =75, S = 24, and n = 36, and assuming that the population is normally distributed, construct a 95% confidenceinterval estimate of the population mean, ยต.

A laboratory tested eleven chickens and found that the mean amount of cholesterol was 244 milligrams with s = 24.92 milligrams. Construct a 95 percent confidenceinterval for the true mean cholesterol content of all such eggs. Assume that the population has a normal distribution.

Use the given degree of confidenceand sample data to find a confidenceinterval for the population standard deviation o. Assume that the population has a normal distribution.
Weights of men: 90% confidence; n=14, Xbar=160.9lb, s=12.6lb

A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below.
Grades
80
90
91
62
77
I am interested in the overall performance for all candidates of a B.S. degree. The populati

Use the given confidence level and sample data to find (a) the margin of error and (b) the confidenceinterval for the population mean. Assume that the population has a normal distribution.
Weight lost on a diet: 99% confidence; n = 61, x = 3.0 kg. s = 5.7 kg.
(a) E = ______kg (Round to one decimal place)
(b) What is t