Statistics and Probability Answers

find the class boundaries, midpoint, and width for the class 12.4-15.2

State whether the following statement true or false

QUESTION 4

The number of arrivals per minute at a bank located in the central business district of a large city

was recorded over a period of 200 minutes, with the following results:

Arrivals Frequency

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

The probability of at least two arrivals per minute at the bank is 0:155:

QUESTION 26

A local fire station receives on average 8.5 emergency telephone calls per hour. Assume that

these calls are Poisson distributed. Calculate the probability that

(a) the fire station will get nine calls during one hour. (2)

(b) the fire station will get five to seven (inclusive) calls during one hour. (3)

(c) the fire station will get at least 4 calls during one hour. (3)

(d) the fire station will get more than 6 calls during one hour.

QUESTION 25

Suppose that X is a binomial random variable with n D 25 and p D 0:5: Calculate

(a) the probability P .X D 15/: (2)

(b) the probability P .X  16/: (4)

(c) the expected value of X. (2)

(d) the variance of X. (3)

QUESTION 24

According to a report from the research for Studying Health System Change, 20% of South Africans

delay or go without medical care because of concerns about cost. Suppose that 8 individuals are

randomly selected.

(a) What is the probability that two individuals will delay or go without medical care? (2)

(b) What is the probability that at most two individuals will delay or go without medical care? (3)

(c) What is the probability that at least seven individuals will delay or go without medical care?

(3)

[8]

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.

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?