Statistics and Probability Answers

1. Suppose IQ scores are normally distributed with mean 100 and standard deviation 10. Which of the following is false?

A. Roughly 68% of people have IQ scores between 90 and 110.
B. A normal probability plot of IQ scores of a random sample of 1,000 people should show a straight line.

C. An IQ score greater than 130 is highly unlikely, but not impossible.

D. An IQ score of 80 is more unusual than an IQ score of 120.


2. A 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders (arachnophobia). At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other. What is the probability that at least one of them suffers from arachnophobia?

A. 72%
B. 82%
C. 42%
D. 62%
E. 52%

(a) According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has (i) Height between 148cm and 175cm (ii) Height above 164cm
(iii) Height below 179cm

Normal distribution about a mean of 60 seconds and a standard deviation of 8 seconds. If 200 patient were selected at random, how many of them could be taken to the hospital in
(a) Less than 50 seconds
(b) more than 64 seconds

The average time taken for the nearest Covid-19 ambulance team to convey a patient showing symptoms to the nearest designated hospital follows the normal distribution about a mean of 60 seconds and a standard deviation of 8 seconds. If 200 patients were selected at random, how many of them could be taken to the hospital in i) Less than 50 seconds (3 Marks) ii) More than 64 seconds (

Jay –Ethan Company is a multi-billion pharmaceutical company that has won a contract by the government to
produce hand sanitizers and respiratory gadgets for frontline health workers in Bono East region. As a result,
the company has decided to give bonuses to its employees to motivate them for the risky task ahead. A sample
of the weekly bonus received by the employees is organized in the table below:
Weekly Bonus ($) 30<35 35<40 40<45 45<50 50<55 55<60 60<56 65<70
Number of employees(f) 8 6 10 5 15 4 9 3
NB: Approximate to 2 decimal places
i) Find the mean amount of bonus given to the employees (4 Marks)
ii) Calculate the standard deviation and interpret it. (4 Marks)
iii) What is the modal amount paid? (4 Marks)
iv) Would you say the bonus distribution follows the standard normal distribution? Why?
(4 Marks)

The shelf life of a particular diary product is is normal distributed with the mean of 12 days and a variance of 9 days. About what percentage of the product will last between 13 to 16 days?

The amount of time that a vehicle spends in a petrol bunk is a random variable with mean, µ
= 4.5 minutes and a standard deviation, σ = 1.8 minutes. Find the probability that on an average
day, the time spend at the petrol bunk is
(a) at most 3.6 minutes
(b) more than 5.5 minutes
(c) at least 3.2 minutes but less than 4 minutes
Compute the value of time spend at the petrol bunk for
(d) 20% of the lower end
(e) 10% of the higher end

QUESTION 2
(a) According to the Ministry of Health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has
i) Height between 148cm and 175cm
ii) Height above 164cm
iii) Height below 179cm
b) The average time taken for the nearest Covid-19 ambulance team to convey a patient showing
symptoms to the nearest designated hospital follows the normal distribution about a mean of 60 seconds and a standard deviation of 8 seconds. If 200 patients were selected at random, how many of them could be taken to the hospital in
i) Less than 50 seconds (3 Marks)
ii) More than 64 seconds (3 Marks)
c) The Shelf life of a particular dairy product is normally distributed with a mean of 12 days and a variance of 9 days. About what percentage of the products last between 13 and 16 days

Cascade Pharmaceuticals Company developed the following regression model, using time-series data from the past 33 quarters, for one of its nonprescription cold remedies:
Y = −1.04 + 0.24X1 − 0.27X2
where Y=quarterly sales (in thousands of cases) of the cold remedy
X1 = Cascade’s quarterly advertising (x $1,000) for the cold remedy
X2 = competitors’ advertising for similar products (x $10,000)
Here is additional information concerning the regression model: sb1 = 0:032
sb2 = 0:070 R2 = 0:64
se = 1:63 F-statistic = 31:402
Durbin-Watson (d) statistic = 0.4995
a. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy?
b. What proportion of the total variation in sales is explained by the regression equation?
c. Perform an F-test (at the 0.05 level) of the overall explanatory power of the model.
d. What additional statistical information (if any) would you find useful in the evaluation of this model?

According to the ministry of health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has