Statistics and Probability Answers

A bank is interested in studying the number of people who use the
ATM located outside its office late at night.On average, 1.6 customers
used the ATM during any 10 minute interval between 9 pm and
Midnight.
i. What is the probability of exactly 3 customers using the ATM
during any 10 minute interval?

ii. What is the probability of 3 or fewer customer using the ATM
during any 20 minute interval?

Let X be a normal random variable with its mean equal to 65 and
standard deviation equal to 12. Find the probabilities for normal
distribution.

1)p(x>48)

2)p(35<x<43)

3)p(x<37)

If electricity power failures occur according to a Poisson distribution
with an average of 3 failures every twenty weeks, calculate the
probability that:
i. at most one failure during a particular week.

ii. exactly 4 failures within ten weeks.

For certain population of students in university, the total students for first,
second and third semester listed according to the faculty, are shown in the
Table 1 below:
Table 1: Total students
Faculty Semester
First Semester Second Semester Third Semester
Engineering 200 150 350
Business 320 110 270
Education 400 340 360

(a) If a students is selected at random, find :
i. The probability of the students from the engineering faculty.

ii. The probability of the students second semester and from
education faculty.

iii. The probability that students from business faculty given that the
students third semester.

A dice is thrown 5 Times . What is the probability of getting sum 25 ?

2. Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers. To determine whether driving experience is related to the number of car accidents, you survey a random sample of 12 Torontonians and ask them about the number of years they have been driving, and the number of car accidents they have been involved in during the past year. The data are presented below:

Driver # of years driving (X) # of car accidents (Y)
A 4.5 3
B 2.5 5
C 1.5 3
D 3 3
E 1.5 6
F 5 2
G 5 0
H 2 4
I 3 1
J 4 2
K 1 5
L 3 2

a. Determine whether the assumptions of car insurance companies are valid. Assuming α=0.05, include the hypotheses for a one-tailed test, critical test statistic, conclusion, and all formulas and calculations.
b. Is it appropriate to conclude that lack of driving experience causes accidents? Why or why not?

b) The height of 40 students were measured and recorded as follows;

38.7 40.2 55.4 60.9 70.1 72.5 50.4 63.7
39.4 54.6 59.3 60.2 45.1 66.5 37.9 74.2
44.5 59.6 55.2 60.7 68.0 70.0 71.2 48.3
49.4 54.4 60.9 64.7 69.3 57.4 46.2 68.9
55.3 70.2 71.7 63.2 55.4 39.0 40.3 44.5
Using classes of 35-39, 40-44,- - - calculate;
i. The arithmetic mean
ii. The standard deviation

At the end of a statistics course, Diana sits for two written papers, P1 and P2 and hands in
a piece of course work. Her marks out 100 were 76 for P1 and 67 for P2 and she gained
81 marks for her course work. Her overall percentage is to be weighted so that the two
written papers account for 40% while the course work accounts for 20%.Calculate
Diana’s overall percentage mark.

The variation of incomes of executives is to be compared with the variation of incomes of
unskilled employees. For a sample of executives, mean = Ksh 500,000 and
Standard deviation = Ksh 50,000. For a sample of unskilled employees, the
mean = Ksh 12,000 and standard deviation = Ksh 2000.
Is the variation among the executives greater than the variation among the unskilled
employees? Justify you answer.

A group of students has measured the heights of 90 trees. The class calculate the mean
height to be x = 12.4 m with standard deviation s = 5.35 m. One student notices that
two of the measurements, 44.5 m and 43.2 m, are much too big and must be wrong.
(a) How many standard deviations away from the mean of 12.4 is the value
44.5?(3m
arks)
191
The incorrect measurements of 44.5 m and 43.2 m must be removed from the data.
(b) Calculate the new value of x after removing the two unwanted values.