Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
Instruction for Submission:
 This is the Second assignment, the deadline for this
assignment is Saturday 9 December 2023 @ 11:59 PM.
 Be ready (with your answers and PDF) before proceeding to enter
the assignment answers on google form as for each student, there
will be only one submission, so make sure of the answers before
submitting your assignment.
 This Assignment consists of two parts Part 1 will be submitted in
the google form as a pdf file of your scanned answers. Part 2 is
MCQ will be submitted by filling out choices in the google form.
 The Submission of the answers will be over the google form, the
URL is
https://docs.google.com/forms/d/e/1FAIpQLScF3MbUB0z4HzjJdo4K
RycamrddH1eXHphorRG_L8Fyygb7DA/viewform
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
Part 1:
Solve the following questions and upload your scanned detailed
answers to google class as pdf file- The first page of the pdf should
contain your Name, ID and Group.
1- An economist uses the price of a gallon of milk as a measure of
inflation. She finds that the average price is $3.82 per gallon and the
population standard deviation is $0.33.You decide to sample 40
convenience stores, collect their prices for a gallon of milk,
and compute the mean price for the sample.
a. What is the probability that the sample mean is between $3.78 and
$3.86?
b. What is the probability that the difference between the sample mean
and the population mean is less than $0.01?
c. What is the likelihood the sample mean is greater than $3.92?
2- Over the past decade, the mean number of members of the
Information Systems Security Association who have experienced a
denial-of-service attack each year is 510, with a standard
deviation of 14.28 attacks. Suppose these attacks follow a normal
distribution.
a. What is the probability of finding more than 550 attacks?
b. What is the likelihood this group will suffer an average of more than
600 attacks in the next 10 years?
c. Compute the probability the mean number of attacks over the next 10
years is between 500 and 600.
d. What is the possibility they will experience an average of less than
500 attacks over the next 10 years?
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
3- Bob Nale is the owner of Nale’s Quick Fill. Bob would like to
estimate the mean number of gallons of gasoline sold to his customers.
Assume the number of gallons sold follows the normal distribution with
a population standard deviation of 2.30 gallons. From his records, he
selects a random sample of 60 sales and finds the mean number of
gallons sold is 8.60.
a. What is the point estimate of the population mean?
b. Develop a 99% confidence interval for the population mean.
c. Interpret the meaning of part (b).
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
Part 2:
You will submit the final answers of this part over the google form.
Solve the questions offline before going into the form.
Be ready (with your answers) before proceeding to enter the
assignment answers.
Don’t click submit unless you are sure of your answers.
MCQ:
1- The primary reason for standardizing random variables is to measure
variables with
a. different means and standard deviations on a non-standard scale.
b. different means and standard deviations on a single scale.
c. dissimilar means and standard deviations in like terms.
d. similar means and standard deviations on two scales.
2- If the value of the standard normal random variable Z is positive, then
the original score is where in relationship to the mean?
a. Equal to the mean
b. To the left of the mean
c. To the right of the mean
d. None of these choices
3- The normal distribution is a
a. discrete distribution with two parameters.
b. binomial distribution with only one parameter.
c. density function of a discrete random variable.
d. continuous distribution with two parameters.
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
4- The standard deviation
of a probability distribution is a measure of
a. variability of the distribution.
b. central location.
c. the shape of the distribution.
d. skewness of the distribution.
5- Given that Z is a standard normal variable, the value z for which P(Z z)
= 0.2580 is
a. 0.70.
b. 0.758.
c. -0.65.
d. 0.242.
6- The time it takes a car maintenance center to repair a car follows a
normal distribution with a mean of 50 minutes and a variance of 144
minutes. The center closes at 4 pm every day. If the mechanical starts
repairing at 3 pm, what is the probability he will finish his repair before he
closes for the day?
a. 0.796
b. 0.830
c. 0.802
d. 0.785
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
7- A corporation makes CV joints for automobiles. An integral part of CV
joints is the bearings that allow the joints to rotate differentially. Once
application utilizes six bearings in a CV joint that have an average
diameter of 2.5 cm. the consistency of the diameters is vital to the
operation of the joint. The specifications require that the variance of these
diameters be no more than 0.0015 cm2. The diameter is continually
monitored by the quality control team. Samples of size 10 are obtained
every day. One of these samples produced bearings that had a variance of
0.00317 cm2. Construct a 95% confidence interval for the true population
variance of the diameters based on the variance obtained for this sample.
a. Between 0.0015 and 0.0106
b. Between 0.015 and 0.016
c. Between 0.38 and 0.129
d. Between 0.038 and 0.1029
8- The standard deviation of is usually called the
a. standard error of the mean.
b. standard error of the sample.
c. standard error of the population.
d. randomized standard error.
9- A recent federal report indicated that 27% of children ages 2 to 5 ate a
vegetable at least five times a week. How large a sample is needed to
estimate the true population proportion within 2% with a 95% level of
confidence?
a. 1890
b. 1891
c. 1892
d. 1893
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
10- What does a 95% confidence interval for the population mean
represent?
a) The range of values within which the sample mean is likely to fall
b) The range of values within which the population mean is likely to
fall
c) The range of values within which the standard error is likely to fall
d) The range of values within which the sample variance is likely to
fall
11- If the sample size is increased, what happens to the width of the
confidence interval for the population mean?
a) It increases
b) It decreases
c) It remains the same
d) It depends on the confidence level
12-What is the confidence level of a confidence interval?
a) The probability that the interval contains the true parameter value.
b) The proportion of samples that will produce an interval that
contains the true parameter value.
c) The margin of error of the interval.
d) The width of the interval.
13- What is the relationship between the confidence level and the margin
of error of a confidence interval?
a) They are directly proportional; as one increases, the other also
increases.
b) They are inversely proportional; as one increases, the other
decreases.
c) They are independent; changing one does not affect the other.
d) They are dependent; changing one may or may not affect the other
depending on the sample size and standard deviation.
Cairo University,
Faculty of Computers and Artificial Intelligence,
Probability and Statistics – 2
Instructor: prof. Ihab El-Khodary
2023-2024
Assignment#2
14- How do you construct a 95% confidence interval for the mean of a
population with unknown standard deviation, using a sample of size n?
a) Use the sample mean as the point estimate and the sample standard
deviation as the standard error, and multiply by the z-score
corresponding to 95% confidence level.
b) Use the sample mean as the point estimate and the sample standard
deviation divided by the square root of n as the standard error, and
multiply by the z-score corresponding to 95% confidence level.
c) Use the sample mean as the point estimate and the sample standard
deviation as the standard error, and multiply by the t-score
corresponding to 95% confidence level and n-1 degrees of
freedom.
d) Use the sample mean as the point estimate and the sample standard
deviation divided by the square root of n as the standard error, and
multiply by the t-score corresponding to 95% confidence level and
n-1 degrees of freedom.
15- What is the relationship between the standard error and the width of
the confidence interval?
a) They are directly proportional
b) They are inversely proportional
c) They are unrelated
d) It depends on the sample size