Statistics and Probability Answers

(2c) 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.

(2b) 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

(2a). 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

The blood pressures, Y (mmHg), and
Ages, X (years) of 10 hospital patients were sampled from a senator’s State and summarized below.
Patient A B C D E F G H I J
Age (X) in Years 20 25 50 30 45 60 10 15 35 70
BP(Y) in (mmHg) 80 85 125 90 100 135 80 70 100 140
Use the table to answer the questions that follow;
i) Calculate the product moment correlation coefficient for the data and interpret your result.
(ii) 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.
iii) Give a reason to support fitting a regression model of the form

(2b). 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.

(2a). 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

An archer shoots arrows at a circular target where the central portion of the target inside is called the bull. The archer hits the bull with probability 1/32. Assume that the archer shoots 96 arrows at the target, and that all shoots are independent. What is an approximated probability that an archer hit not more than one bull?

The mean number of errors due to a bug occurring in a minute is 0.0001. What is the probability that no error will occur in 20 minutes?

Suppose a special type of small data processing firm is so specialized that some have difficulty making a profit in their first year operation. The pdf that characterizes proportion Y that makes the profit is given by:

f(y)= Ky(1-y)2 0< y < 1
(a): What is the value of “K” that renders the above a valid density function?
(b): Find the probability that at most 40% of the firms make a profit in the first year.