In April 2025
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When coIIecting the premiums, lnsurance rounds 60,000 motor insurance premiums to the nearest ten doIIars.
(a) Stating any assumptions that you have made, calculate the probabiIity that the totaI premiums coIIected wiII be aItered by more than $500 from the originaI vaIue (before rounding off). Show aII detaiIs of your working.
(b) Comment, whether or not Apex lnsurance shouId be worried that the amount aItered with this rounding exceeds $2000? Explain.
Box A and Box B both contain the numbers 2, 4, 6 and 8. Construct the probability mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacement.
A company producing lubricating oil that the average content of the containers is 20 litres. Test this claim if a random sample of ten containers are 20.5, 19.4, 20.2, 19.8, 20.6, and 19.6 litres .assume normal distribution and use 1% level of significance
the mean serum cholesterol level of a large population of overweight children is 220 mg per deciliter (mg/dl), and the standard deviation is 16.3 mg/gl. If a random sample of 35 over which children is selected, find the probability that the mean will be between 220 and 222 mg/ dl. Assume the serum cholesterol level variable is normally distributed.
A population consists of the values (1, 2, 4). List down all the possible samples of size 2 that can be drawn from this population with replacement.
A population consists of the values (1, 2, 4). List down all the possible samples of size 2 that can be drawn from this population with replacement.
1. A certain research center requires an IQ score above 131.5.
Assume IQ scores are normally distributed with mean of 100 and standard
deviation of 15. Nine candidates took IQ tests. Find the probability that the IQ
score of a randomly chosen individual is at least 131.5?
2. A Company which produces cigarettes claims that it has now reduced the
amount of nicotine. The Supporting evidence consists of a random sample of 40
cigarettes and gives mean amount of nicotine 0.941 g and a standard deviation of
0.313g. What is the probability that mean nicotine amount is greater than 0.882 g.
1. A system is tested for faults once per hour. If there is no fault, none
will be detected. If there is a fault, the probability is 0.8 that it will be detected. The
tests are independent of one another.
a) If there is a fault, what is the probability that it will be detected in 1 hour or less?
b) If there is a fault, what is the probability that it will be detected in 3 hours or
less?
c) What is the mean number of tests that must be conducted in order to detect a
fault?
2. The number of hits on a website follows a Poisson process with a
rate of 3 per minute.
a) What is the probability that more than a minute goes by without a hit?
b) If 2 minutes have gone by without a hit, what is the probability that a hit will
occur in the next minute?
Compute the 95 percent interval estimate of ų given ó = 9, n=40 and x= 115
Construct the sampling distribution of the sample means. Then compute for the mean of the sample
means. (12points)
