Statistics and Probability Answers

Jon's grades from reading class are shown below.
78, 83, 87, 72, 91, 85, 93, 79, 100
What is the range of Jon's grades from reading class?

The weekly incomes of a large group of middle managers are normally distributed with a
mean of K800 and a standard deviation of K85.
(i) What is the probability of finding a middle manager with a weekly income of
between K840 and K900?
(ii) What is the percent of middle managers that earn more than K905?
(iii) What is the percent of middle managers that earn less than K905?
(iv) What is the probability of finding a middle manager with weekly income of
between K750 and K850?
(v) What is the probability of finding a middle manager with a weekly income of
between K700 and K790?
(vi) Above what income would the top 10% of the managers earn?
(vii) Below what income would the lowest 10% of the managers earn?

Advertisement is a key determinant of revenue from sales in the plywood business. If the relationship between the two is specify as , where the dependent variable (Y) is sales revenue and the independent variable (X) is advertisement, use the table below to answer questions that follow.
Revenue (Sales)
100
90
80
110
60
50
55
65
40

Advertisement
10
12
8
15
18
20
25
22
30


Estimate the regression equation (8 Marks)
Interpret the parameters. ( 2 Marks)
Predict the amount of revenue that will be generated when advertisement is $40
(2 Marks)
Estimate the coefficient of determination and interpret (4 Marks)

It is argued that the temperature condition is highly correlated with crop harvest in the tomatoes business. The information from north eastern Ghana is summarized in the table below. Use the table to answer the questions that follow
Yield (crop)
40
50
70
65
80
45
90
100
120

Temperature
10
15
20
25
21
28
30
31
35

Calculate the pearsons correlation coefficient and interpret it (8 Marks)
Did the result support past argument?

It is argued that the temperature condition is highly correlated with crop harvest in the tomatoes business. The information from north eastern Ghana is summarized in the table below. Use the table to answer the questions that follow
Yield (crop)
40
50
70
65
80
45
90
100
120

Temperature
10
15
20
25
21
28
30
31
35

Calculate the pearsons correlation coefficient and interpret it.
Did the result support past argument?

A market research company informs a prospective mini marker entrepreneur that the average income per household in the region is RM60 000 per annum. The household income is assumed to be normally distributed with standard deviation of RM7000, based on an early study. For a random sample of 130 households, the mean household income is found to be RM47 000. Test the null hypothesis that the population mean household income is RM60 000 at 5 percent significance level.

On a given day, each computer in the lab has at most one crash. There is a 5% chance
that a computer has a crash during the day, independent of the performance of any
other computers in the lab. Find the probability that on any given day, there are;
(a) exactly 3 crashes
(b) at most 3 crashes
(c) at least 3 crashes
(d) more than 3 and less than 6

Weights of students are normally distributed with a mean of 55 kg and a variance of 9 kg.
a. Find the probability that the weight of one randomly selected student is less than 48 kg.
b. Find the probability that the mean weight of 16 randomly selected students is more than 57 kg.
c. Find the median of the weight of students

The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time. Test at 5% the null hypothesis that the rate of emissions is unchanged.

In your own words the fundamental counting principle and explain why it’s useful in probability