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If A, B and C are any sets in a sample space S, shade each of the following on separate Venn diagrams

1. š“ ∩ (šµ ∩ š¶)

Ģ…Ģ…Ģ…Ģ…Ģ…Ģ…Ģ…Ģ…Ģ…Ģ… [2]

2. The complement of B intersect A union the intersection of A and C



The following sample of eight measurements was randomly selected from a normally distributed population: 12, 10, 9, 8, 15, 10, 11, and 13. Test for significant difference between the sample mean and the population mean of 10. Use š›¼ = 0.05.


Drinking water has become an important concern among people. The quality of drinking water must be monitored as often as possible during the day for possible contamination. Another variable of concern is the pH below 7.0 is acidic while a pH above 7.0 is alkaline. A pH of 7.0 is neutral. A water-treatment plant has a target pH of 8.0. Based on 16 random water samples, the mean and the standard deviation were found to be 7.6 and 0.4, respectively. Does the sample mean provide enough evidence that it differs significantly from the target mean? Use š›¼ = 0.05, two – tailed test.



Imelda got a score of 98,16,17,89,22,14,21,34,56 in her last quiz in midterm. What is her average score?

Find the probability of the indicated event if P(E)=0.35 and P(F)=0.45

find P(E or F) if P(E and F) = 0.05

P(E or F)=


For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 36 beats per minute


The College of Agriculture obtained the following data representing the one-week growth in centimeters of 20

newly planted soybean plants:

1.3

4.9

3.9

0.8

4.1

1.1

3.1

2.2

2.4

2.4

2.4

3.9

1.8

3.9

3.9

4.1

3.9

2.4

4.0

4.2

Find the following:

a. MeanĀ 

b. MedianĀ 

c. ModeĀ 

d. VarianceĀ 

e. Standard DeviationĀ 

f. RangeĀ 


A quality-control manager at an amusement park feels that the amount of time that people

spend waiting in line to ride the roller coaster is too long. To determine if a new loading

and unloading procedure is effective in reducing the wait time, she measures the amount

of time (in minutes) people are waiting in line for seven days. To make a reasonable

comparison, she chooses times when weather conditions are similar. (12 points)


Mon Tues Wed Thurs Fri Sat Sun

2 p.m. 2 p.m. 2 p.m. 2 p.m. 2 p.m. 4 p.m. 12 noon

Wait time before, X1 12 26 20 38 57 82 57

Wait time after, X2 11 28 19 36 59 75 55


Is the new loading and unloading procedure effective in reducing the wait time at the

α = 0.05 level of significance?


a. State the hypothesis and identify the claim of the researcher.

b. Find the critical value(s).

c. Compute the test value.

d. Make a decision on the null hypothesis.

e. Make a decision on the claim of the researcher.


If a bag contains 6 red balls and 8 blue balls, and you pull one ball from the bag, which is blue, what is the probability that the next ball you pull will be red?


A quality-control manager at an amusement park feels that the amount of time that people spend waiting in line to ride the roller coaster is too long. To determine if a new loading and unloading procedure is effective in reducing the wait time, she measures the amount of time (in minutes) people are waiting in line for seven days. To make a reasonable comparison, she chooses times when weather conditions are similar.


Mon. Tues. Wed. Thurs. Fri. Sat. Sun

2 pm. 2 pm. 2 pm. 2 pm. 2 pm. 4 pm. 12 noon


Wait time before x1 12. 26. 20. 38. 57. 82 57

Wait time before x2. 11. 28. 19. 36. 59. 75. 55


Is the new loading and unloading procedure effective in reducing the wait time at the α = 0.05 level of significance?


a. State the hypothesis and identify the claim of the researcher.Ā 

b. Find the critical value(s).Ā 

c. Compute the test value.Ā 

d. Make a decision on the null hypothesis.Ā 

e. Make a decision on the claim of the researcher.Ā 




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