Search & Filtering
Question 3
In a typical month, an insurance agent presents life insurance plans to 40 customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the relevant information, answer the following questions:
(i) What is the probability that exactly 5 customers will buy life insurance from this agent in the coming month?
(ii) What is the probability that no more than 10 customers will buy life insurance from this agent in the coming
month?
(iii) What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
(iv) Determine the mean and standard deviation of the number of customers who will buy life insurance from
this agent in the coming month.
1. Ecobank Ghana issues its own credit card. The credit manager,
Giovina wants to find whether the mean monthly unpaid
balance is not at most Ghc400. The level of significance is set
at 0.05. A random check of 25 unpaid balances revealed that
the average is GHc410 with the standard deviation of GHc20.
Should the credit manager conclude that the population mean
is not at most GHc400, or is it reasonable that the difference is
due to chance?
a. Explain why t is the test statistic to be used here.
b. What is the critical value of the test statistic?
c. What is your decision regarding the H0?
d. Estimate the p-value and use it to decide.
e. Should the credit manager conclude that the population
mean is not at most GHc400, or is it reasonable that the
difference is due to chance? Explain briefly.
(i) What is the probability that exactly 5 customers will buy life insurance from this agent in the coming month?
(ii) What is the probability that no more than 10 customers will buy life insurance from this agent in the coming month?
(iii) What is the probability that at least 20 customers will buy life insurance from this agent in the coming month?
(iv) Determine the mean and standard deviation of the number of customers who will buy life insurance from this agent in the coming month.
Before After
128 135
105 110
119 131
140 142
98 105
123 130
127 131
115 110
122 125
145 149
At the 0.01 significance level:
a) Make your decision using the critical value approach.
b) What is the p-value? Decide with it
c) Mention one assumption that needs to be made about the distribution of the differences?
d) Is the change of government associated with the higher prices of residential homes? Justify practically.
Before After
128 135
105 110
119 131
140 142
98 105
123 130
127 131
115 110
122 125
145 149
At the 0.01 significance level:
a) Make your decision using the critical value approach.
b) What is the p-value? Decide with it
c) Mention one assumption that needs to be made about the distribution of the differences?
d) Is the change of government associated with the higher prices of residential homes? Justify practically.
(i). Indicate whether the decision taken is right or wrong, giving reasons for your answer.
(ii). Base on your decision taken in (i) above, explain the probability concept that the gambler employed in playing the game.
7. A telephone exchange has two long distance operators. The telephone company finds that during the peak load long distance calls arrive in a Poisson fashion at an average rate of 15 per hour. The length of service on these calls is approximately exponentially distributed with mean length 5 Minutes
(What is the probability that a subscriber will have to wait for his long distance call during the peak hours of the day?
Dif the subscribers will wait and are serviced in turn, what is the expected waiting time?
Tourists enter a popular game reserve at an average rate of one every five minutes. What is the probability that exactly ten tourists arrive within the first hour?
57 64 54 94 38 61
50 39 94 63 59 31
68 88 93 48 82 82
74 70 92 76 98 91
32 33 31 75 54 48
36 64 63 66 92 98
36 54 71 86 84 55
91 34 64 67 89 78
97 92 53 56 68 55
93 42 51 77 36 93
44 66 63 33 68 79
83 53 86 76 35 40
55 41 36 39 42 96
60 53 38 51 95 56
48 69 49 33 95 37
83 62 96 34 85 32
39 59 77 62 35 34
54 89 36 45 83 34
39 61 88 86 55 33
69 54 30 38 79 77
95 34 38 91 80 90
88 45 95 71 80 43
61 40 31 61 58 53
91 63 60 94 98 53
50 34 75 74 90 98
Make the frequency distribution table with appropiate class interval, frequency,
cumulative frequency.
b. Calculate the mean, median, mode and quartiles of grouped data.
c. Calculate the standard deviation, variance and range
d. Make the following diagrams: Histogram, Frequency Polygon, Ogive
#339914 on Dec 2023