Statistics and Probability Answers

Using Minitab Test the hypothesis that the average dissolution time is 20 seconds, using the random sample of dissolution times below.
Dissolution time (secs): 23 19 26 22 18 27

At a university, the average cost of books per student has been $400 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $400. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $430 with a standard deviation of $80. What is the test value for this hypothesis test?

Heights of men on a baseball team have a bell shaped distribution with a mean of 179 and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of men between the following values.

A. 172 cm and 186 cm
B 158 cm and 200 cm

A. What percentage of the men are between 172 cm and 186 cm
B. What percentage of the men are between 158 cm and 200 cm

If two events are exhaustive, does it also means that they are mutually exclusive? Can you explain what is their differences?

if the mean lifespan of an insect is 144 days and the standard deviation of its lifespan is 16 days find the probability that the next insect studied lives less than 140 days

Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,125 per hour and a standard deviation of $280.

What is the operating cost for the lowest 6 percent of the airplanes? (Round z value to 2 decimal places. Omit the "$" sign in your response.)

Software filters rely heavily on “blacklists” (lists of known “phishing” URLs) to detect fraudulent e-mails. But such filters typically catch only 20 percent of phishing URLs. Jason receives 14 phishing e-mails.

(a)
What is the expected number that would be caught by such a filter? (Round your answer to the next whole number.)

Expected number

(b)
What is the chance that such a filter would detect none of them? (Round your answer to 5 decimal places.)

Probability

Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 14 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 54 returns. What is the probability that she makes errors on:

(a)
More than 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Probability

(b)
At least 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Probability

(c)
Exactly 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Probability

A town-planning sub-committee in Tshwane wanted to know if there is any difference in the mean travelling time to work of car and Train commuters. They there carried out a survey amongst car and bus commuters and with the following sample statistics:
Car Commuters
Train Commuters
X1= 29.6 min
X2 = 25.2 min
S1= 5.2 min
S2= 2.8 min
N1=22 drivers
N2=36 passengers
4.1 Test the hypothesis at the 5% significance level that it takes car commuters to get to work earlier than Train commuters.

The records of 400 examinees are given below:
Score
Educational Qualification
Total
Diploma
Degree
I.T
Below 50
90
30
60
180
Between 50 and 60
20
70
70
160
Above 60
10
30
20
60
Total
120
130
150
400
If an examineer is selected at random from this group, find:
1.1.1 The probability that he is a Diploma graduate.
1.1.2 The probability that he is a Degree graduate, given that his scores are above
60.
1.1.3 The probability that his score is below 50, given that he’s doing IT.
1.2 A marketing manager makes the statement that the long-run probability that a
customer would prefer the deluxe model to the standard model is 30%.
1.2.1 What is the probability that exactly 3 in a random sample of 10 customers will
prefer the deluxe model?
1.2.2 What is the probability that more than 2 in a random sample of 10 customers
will refer the standard model?