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QUESTION 21
Let X represent the number of children in a randomly selected South African household. The
probability distribution of X is given below.
x 1 2 3 4 5
P .x/ 0:25 0:33 0:17 0:15 0:10
(a) What is the probability that a randomly selected South African household will have more than
2 children? (3)
(b) What is the probability that a randomly selected South African household will have between
2 and 4 children (inclusive)? (3)
(c) What is the probability that a randomly selected South African household will have fewer than
4 children? (3)
(d) Calculate the expected number of children in a randomly selected South African household.
(4)
(e) Calculate the variance of the number of children in a randomly selected South African house-
hold. (5)
[18]
The regular price for a pair of shoes is $245. They are currently on sale for 25% off. The harmonized sales tax in Ontario is 13%. Your receipt shows that the final cost is $ 215.32. Are you happy with the final cost? Explain why or why not. Complete without a calculator and show your work.
Form the partial differential equation by eliminating the function ϕ and Ψ from z=ϕ(x+iy) +Ψ(x-iy)
The time taken to complete a particular type of job is distributed approximately normally with mean 1.8 hours and standard deviation 0.1 hours. (a) If normal-time work finishes at 6.00 p.m. and a job is started at 4.00 p.m., what is the probability that the job will need overtime payments? (b) What estimated completion time (to the nearest minute) should be set so that there is a 90% chance that the job is completed on time?
A popular restaurant has places for 50 customers. For Sunday lunches there is great demand so it is necessary to book. The restaurant manager knows that 10% of customers who book do not arrive at the restaurant. He takes bookings for Sunday lunch for 55 customers. What is the probability that he will have more customers than places?
1)A cab driver knows from experience that the number of fares he will pick up in an evening is a random variable with µ = 21.3 and s = 3.4 Assuming that the distribution of this random variable can be approximated closely with a normal curve, find the probabilities that in an evening the driver will pick up (a) at least 30 fares (b) anywhere from 20 to 25 fares inclusively.
Consider all possible samples of size 2 that can be drawn with replacement from the population 1, 5, and 8. Compute the following:
1. Population mean
2. Population variance
3. Population standard deviation
4. Illustrate the probability histogram of the sampling distribution of the means
Arcs of quarter circles are drawn inside the square. The center of each circle is at the corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20cm. Find the area, in square cms, common to the four circular quadrants.
Consider all possible samples of size 3 that can be drawn without replacement from the population 1, 5, and 8, 6, 10. Compute the following:
1. Population mean
2. Population variance
3. Population standard deviation
4. Illustrate the probability histogram of the sampling distribution of the means
1. A supermarket owner believes that the
mean income of its customers is P50,000
per month. One - hundred customers are
randomly selected and asked of thei r
monthly income. The sample mean is
P48,500 per month and the standard
deviation is P3,200. Is there sufficient
evidence to indicate that the mean
income of the customers of the
superma rket is P50,000 per month? Use
�� = 0.05.
#331389 on Nov 2022