Question

May I have the answers for the following questions step by step please.

1. Annual sales, in millions of euros, for 21 pharmaceutical companies follow.

          8408               1374               1872               8879               2459               11413             608

14138 6452 1850 2818 1356 10498 7478

4019 4341 739 2127 3653 5794 8305

1. Provide a five-number summary.
2. Compute the lower and upper limits for the box plot.

2. Suppose that IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of

15.

1. What percentage of people have an IQ score between 85 and 115?
2. What percentage of people have an IQ score between 70 and 130?
3. What percentage of people have an IQ score of more than 130?
4. A person with an IQ score greater than 145 is considered a genius. Does the empirical rule support this statement? Explain.

3. A sample has data values 27, 25, 20, 15, 30, 34, 28, 25. Calculate the range, interquartile range, variance, standard deviation and coefficient of variation.

4. Use the below table to answer the questions:

	Fatalities	Serious injuries	Total
Children	53	1976	2029
Adults	1722	19056	20778
Total	1775	21032	22807

1. What is the probability that the victim has fatalities?
2. What is the probability that the victim was an adult and he/she has serious injuries?
3. What is the probability that the victim was a child or he/she has fatalities?
4. What is the probability of a serious injury given the victim was a child?
5. What is the probability that the victim was an adult given a fatality occurred?

5. A company is about to sell to a new client. It knows from past experience that there is a real possibility that the client may default on payment. As a precaution the company checks with a consultant on the likelihood of the client defaulting in this case and is given an estimate of 20%. Sometimes the consultant gets it wrong. Your own experience of the consultant is that he is correct 70% of the time when he predicts that the client will default but that 20% of clients who he believes will not default actually do. What is the probability that the new client will not default?

Answer 1

( a )

Five number summary :

• The minimum value of the data set is 608.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

608   739   1356   1374   1850   1872   2127   2459   2818   3653   4019   4341   5794   6452   7478   8305   8408   8879   10498   11413   14138   

So, the bottom half is

608   739   1356   1374   1850   1872   2127   2459   2818   3653   

• The first quartile is = 1861

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

608   739   1356   1374   1850   1872   2127   2459   2818   3653   4019   4341   5794   6452   7478   8305   8408   8879   10498   11413   14138   

• So, the median is 4019 .

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

608   739   1356   1374   1850   1872   2127   2459   2818   3653   4019   4341   5794   6452   7478   8305   8408   8879   10498   11413   14138   

So, the upper half is

4341   5794   6452   7478   8305   8408   8879   10498   11413   14138   

• The third quartile of the data set is 8356.5.
• The maximum value of the data set is 14138.

( b )

IQR=8356.5−1861=6495.5

• Lower limits

=Q1−(1.5⋅IQR)

=1861−(1.5⋅6495.5)

=7882.25

• Upper limits

= Q3+(1.5⋅IQR)

= 8356.5+(1.5⋅6495.5)

= 18099.75