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A card is drawn from a deck, then replaced, and a second card is drawn. Find the probability of selecting
- two pictures card
- a black card and an ace card
- a diamond and a king
- a lettered card and a number card
- a spade and a club
A clothing company produces men’s jeans. The jeans are made and sold with either a regular cut or a boot cut. In an effort to estimate the proportion of their men’s jeans market in Chilanga City that prefers boot-cut jeans, the analyst takes a random sample of 212 jeans sales from the company’s two Chilanga City retail outlets. Only 34 of the sales were for boot-cut jeans. Construct a 90% confidence interval to estimate the proportion of the population in Chilanga City who prefer boot-cut jeans.
A random sample of 10 students contains the following observations, in hours, for time spent studying in the week before final exams.
28 57 42 35 61 39 55 46 49 38
Assume that the population distribution is normal
(i) Find the sample mean and standard deviation
(ii) Test, at the 5% significance level, the null hypothesis that the population mean is 40 hours against the alternative that it is higher
Six years ago Olwethu lent Happy R150 000 on condition that he would pay her back in nine years time. The applicable interest rate is 15,5% per year, compounded monthly. Happy also owes Olwethu another amount of R250 000 that he has to pay back six years from now for a loan that earned interest at 16,4% per year, compounded semi-annually. Happy asks Olwethu if he an settle both his debts three years from now. The total amount that Happy will have to pay Olwethu three years from now is
A sample of 40 children from Kafue state showed that the mean time they spend watching television is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 35 children from Chilanga showed that the mean time spent by them watching television is 23.5 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent watching television by children in Kafue state is greater than that for children in Chilanga? Assume that the standard deviations for the two populations are equal [10 marks] Question
Question 1
The lifetimes of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer’s output
a. What is the mean of the sample mean life?
b. What is the variance of the sample mean?
c. What is the standard error of the sample mean?
d. What is the probability that, on average, those nine light bulbs have lives of fewer
than 1,050 hours?
There are 150 students in a class. The distribution if their marks in a mathematics test are as follows
Class frequency
0-9 3
10-19 10
20-29 17
30-39 x
40-49 35
50-59 y
60-69 18
70-79 10
80-89 5
90-99 2
Required
Use the ogive to estimate
i) The 8th decile (2marks)
ii) The 7-th percale (2marks)
iii) The lower quartile
An interest rate of 14,90% per year,
compounded every 3 months. What is equivalent interest rate compounded weekly?
2x+y-z=8
-3x-y+2z=-11
-2x+y+2z=-3
Let R1 and R2 be two relation on real number such that R1 = {(x, y)|x < y} and R2 =
{(x, y)|x > y}, then find R1 ∪ R2,R1 ∩ R2,R1 − R2, R2 − R1, and R1
LR2.
#339914 on Dec 2023