Statistics and Probability Answers

The table below show the time distribution of fifty depositors to finish a transaction with a bank personnel.

Time Number of Depositors (f)
(nearest minute)

23-25 4
20-22 6
17-19 16
14-16 8
11-13 8
8-10 6
5-7 2

Deternine the values of:

a.) mean
b.) median
c.) mode
d.) first quartile
e.) fourth quartile
f.) 80th percentile

To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After).

Subject Before After
1 132 114
2 174 175
3 147 140
4 179 152
5 122 100
6 192 158
7 125 98
8 119 93
9 200 191
10 173 139
Give a 93.1% confidence interval for μB−μA, the difference between LDL levels before and after taking the medication.

Confidence Interval =
at 93.1% confidence.

Give your answer as an open interval, in the form (A,B) where A is the lower bound and B is the upper bound.

Use a pie chart to show the following categorical distribution.
a. People’s Reform Party (1,800)
b. Nationalist People’s Coalition (2,700)
c. Laban ng Demokratikong Pilipino (1,000)
d. Asenso Pilipino Party (4,500)
Relative frequency
0.18
0.27
0.1
0.45
Pf
18
27
1
45

In studying the relationship between loan delinquency and borrower characteristics, a bank found the following information: • 80% of borrowers have been employed at their present job for 3 or more years, • Of the borrowers who have been employed at their present job for 3 or more years, 5% are behind in their payments • Of the borrowers who have been employed at their present job for less than 3 years, 15% are behind in their payments

If a loan account is randomly selected, what is the probability that the borrower has been employed at their present job for less than 3 years AND is behind in their payments? (a) 0.17 (b) 0.03 (c) 0.20 (d) 0.014 (e) 0.24

If a loan account is randomly selected, what is the probability that the borrower has been employed at their present job for 3 or more years OR is not behind in their payments? (a) 0.76 (b) 0.744 (c) 0.97 (d) 0.83 (e) 0.96

If a loan account is randomly selected from a borrower who has been employed at their present job for 3 or more years, what is the probab

7. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 875 hours. A random sample of 58 light bulbs has a mean life of 852 hours with a standard deviation of 95 hours. Do you have enough evidence to reject the manufacturer’s claim? Use a = 0.09.
a. Identify the null hypothesis and alternative hypothesis.
b. Identify the critical value (s). Use a comma to separate answers as needed
c. Identify the standardized test statistic.
d. Decide whether to reject or fail to reject the null hypothesis.

Suppose that 50% of all babies born in a particular hospital are girls. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are girls?

The financial aid director of a large college reports that 32% of the students enrolled are receiving some sort of financial aid. A researcher claims the percentage is lower and finds (from sampling) 20 out of 80 students are receiving some sort of financial aid. At alpha = 0.10, decide whether the financial aid director's report that 32% of the students are receiving some sort of financial aid holds up. For question #21 (multiple choice), choose the alternate hypothesis. For #22, fill in the space provided with your calculated value for p hat. For question #23, fill in the space provided with your calculated Z value from the information provided. For #24, answer True or False with regard to rejecting the null hypothesis.

IQ of professional Pilots
The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Listed below are IQ scores of randomly selected professional pilots. It is claimed that because professional pilots are a more homogeneous group than the general population, they have IQ scores with a standard deviation less than 15. Test that claim using a 0.05 significance level.
Assume that a simple random sample is selected from a normally distributed population.
121 116 115 121 116 107 127 98 116 101 130 114
Identify the null hypothesis:

Alternative hypothesis:
Test statistic:
P-Value or critical value(s):

1) If you have a school report which has 53 rows of assessment criteria.
2) You have 5 marking criteria for each row (in terms of qualitative assessment)
3) What are the chances that a 2008 and a 2009 year report on the same child are exactly the same?
Thanks

A bag contains two red balls, three blue balls and five green balls.
Three balls are drawn at random. Find the probability that
a) the three balls are of different colours
b) two balls are of the same colour
c) all the three are of the same colour.