Statistics and Probability Answers

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 ii) More than 64 seconds

In a certain city the mean price of a litre of milk is 63 cents and the standard deviation is 8
cents. The average price of a loaf of bread is $1.80 and the standard deviation is 15 cents.
At a 24-hour convenience store, a litre of milk costs $0.89 and a loaf of bread costs $2.19.
a. Determine the z-score for each item. *Round your z-score to the nearest hundredth.
MILK BREAD

b. Which item costs relatively more at the convenience store? Explain your answer.

Scores on intelligence tests (IQs) are normally distributed in children. IQs from the Wechsler
intelligence tests are known to have means of 100 and standard deviations of 15.

a. A student scored 122 on the test. Determine the z-score. *Round your z-score to the nearest hundredth.

b. A different student had a z-score of 2.41. Determine this student’s actual mark, to the nearest hundredth, on the test.

A random sample of stipends of teaching assistants in economic is listed. Is there sufficient evidence at the alpha = 0.05 to conclude that the average stipend differs from 15,000. The stipends (in dollars) listed in the figure are for the academic year
14,000 18,000 12,900 14,356 13,185
13,419 14,000 11,981 17,604 12,283
16,338 15,000

an electric researcher tested an air fryer listed are prices of the three types of air fryer at alpha 0.10 is there is a significant difference in the average prices of the three types of the air fryer

watt
1000 900 800
270 240 180
245 135 155
190 160 200
215 230 120
250 250 140
230 200 180
200 140
210 130

If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer.

The weekly incomes of a large group of Fire officers are normally distributed with a
mean of K800 and a standard deviation of K85.
(i) What is the probability of finding a Fire officers with a weekly income of
between K840 and K900?
(ii) What is the percent of Fire officers that earn more than K905?
(iii) What is the percent of Fire officers that earn less than K905?
(iv) What is the probability of finding a Fire officer with weekly income of
between K750 and K850?
(v) What is the probability of finding a Fire officer with a weekly income of
between K700 and K790?
(vi) Above what income would the top 10% of the officers earn?
(vii) Below what income would the lowest 10% of the officers earn?

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 (4 Marks)
ii) Height above 164cm (3 Marks)
iii) Height below 179cm (3 Marks)
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

QUESTION 3
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.
ii) Calculate the standard deviation and interpret it.
iii) What is the modal amount paid?
iv) Would you say the bonus distribution follows the standard normal distribution? Why?
v) Calculate the coefficient of variation for the bonus distribution of Jay-Ethan and compare it with the
coefficient of variation of 19.45% for the bonus distribution of KGH, a subsidiary of Jay-Ethan.

(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