Question

1. The weights in ounces of a sample of rats in a lab are given below.

4, 4, 2, 5, 5, 3, 4, 7, 9, 5

a. Construct a frequency distribution using five classes.

b. Construct a histogram for the above distribution.

c. Find the Mean

d. Find the Median & Mode

e. Find the sample variance and standard deviation (5 points)

2. The probability that a part will malfunction is 0, 1, 2, 3, or 4 or more times in a decade is 0.4, 0.2, 0.2, 0.1 and 0.1 respectively.

a. Construct a probability distribution.

b. Find the mean.

c. Find the variance and standard deviation.

d. Graph ()

Answer 1

Here the given data is weight of rats,

Now,.

a) The Frequency distribution table with five classes is as below,

Frequency Distribution Table
Class	Frequency	realtive Frequency
2 - 3.5	2	0.20
3.6 - 5.1	6	0.60
5.2 - 6.7	0	0
6.8 - 8.3	1	0.10
8.4 - 9.9	1	0.10
Total	10	100.

This is the Frequency distribution table with five classes.

b) From the above frequency distribution table we constructed the histogram as below,

This is the histogram for Frequencies.

Now we need to compute the summary and i computed the summary of Statistics using Statistical software as below,

Your Histogram
Mean	4.8
Standard Deviation (s)	1.98886
Skewness	0.97877
Kurtosis	1.34906
Lowest Score	2
Highest Score	9
Distribution Range	7
Total Number of Scores	10
Number of Distinct Scores	6
Lowest Class Value	2
Highest Class Value	9.9
Number of Classes	5
Class Range	1.6.

  

c) The mean and same Standerd deviation and sample variance is given below,

The mean is calculated as below,

Mean xbar = Sum (Xi) / no. Of obs.

Mean xbar= 48/10

Mean = 4.8

Median is calculated as below,

2,3,4,4,4,5,5,5,7,9

First we arranged the data in assending order then we find median = (4+5)/2

Median = 4.5

Mode is most frequent values in data set,

Mode is 4 and 5.

The sample standerd deviation is 1.98886 and the sample variance is 3.95556. (rounded to 5 decimal places).

2) The discrete probability distribution mean and variance is computed as below,

This is answer of your Question.

Thank you.