Question

Assignment III

1) Use the non-machine formula to calculate the variance and standard deviation from the following data

Herd 1

67 62 69

72 68 68

71 69 65

71 70 64

64 66 71

67 75

2) What is the probability that one card selected from a deck of 52 is a club or a number card or both?

3) A container contains 10 green tennis balls and 7 orange tennis balls. What is the probability of drawing 2 green tennis balls in a row? Draw without replacement.

4) A die is rolled four times what is the probability of rolling 3 twos?

5) A pair of dice is rolled 5 times, what is the probability of 3 sixes?

6) An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.

a) What is the probability Linda Lahey, company president, received exactly 1 email between 4pm and 5 pm yesterday?

b) What is the probability she received 5 or more email during the period?

c) What is the probability she did not receive any email during the period?

7) The personnel manager of Cumberland Pig Iron Company is studying the number of on-the-job accidents over a period of one month. He developed the following probability distribution in the following table. Compute the mean, variance, and standard deviation of the number of accidents in a month.

Number of Accidents	Probability
0	.40
1	.20
2	.20
3	.10
4	.10

Answer 1

Sample

67,62,69,72,68,68,71,69,65,71,70,64,64,66,71,67,75

Standard Deviation =((Xi-Mean)^2/Sample Size)^(0.5)=3.36

Variance =Standard Deviation^2=3.36^2=11.28

Answer for 2)

One Club Card Prob.= 13/52=1/4...(13C1/52C1)

One Number card= 36/52=9/13...(36C1/52C1)

Both =9/52

Answer for 3)

1 st Grenn ball out of the population of 17 balls =10C1/171=10/17

Now 1 ball removed hencec we are left with population of 16 balls

again 2nd ball removed the probabililty will be=9C1/16C1=9/16

Total Probability =10/17*9/16=90/272=45/136

Answer for 4)

Probabillity of Rolling 3 twos

We can arrange these 3 twos in four dice outcme as 4C2*(1)*1*5*5/6^4=6*5*5/1296=25/216