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# Probability, mean, variance, standard deviation,

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1. The Penguin Company employs 400 men and 100 women. Of the male employees, 280 work in the plant, 40 are in the office, and 80 are field salesmen. The female employees are distributed as follows: 20 to the plant, 50 to the office, and 30 to the sales. If the CEO, Stephanie, randomly selects an employee to tour a factory in Japan, what is the probability that he or she is:

Men Women Totals
Plant worker 280 20 300
Office worker 40 50 90
Field salesman 80 30 110
Totals 400 100 500

a. Male?

b. Female?

c. A plant worker?

d. An office worker?

e. A field sales person?

f. A male plant worker?

g. A plant worker given he is male?

h. An office worker given that she is female?

2. Given that a discrete random variable, X, has the following probability distribution:

X 0 1 2 3 4
P(X) .2 .5 .15 .10 .05

a. Find the mean.

b. Find the variance.

c. Find the standard deviation.

3. Population of consumers where 30% of them liked a new product and 70% of them disliked it. If 20 persons are sampled, what are the Binomial probabilities of finding:

a. 8 or fewer consumers who like the product.

b. Precisely 10 consumers who like the product.

c. Fewer than 6 consumers who like the product.

d. More than 7 consumers who like the product.

e. Greater than or equal to 5 but less than or equal to 12 consumers who like the product.

4. Accidents at a chemical plant occur at a rate of 1.5 per month. Find:

a. The expected number of accidents in a year?

b. The probability of no accidents next month?

c. The probability of fewer than three accidents next month?

5. The following distribution shows the prices of books at a college.

Class Frequency (Fi) Class Midpoint (Xi) FiXi
10-20 20 15 300
20-30 25 25 625
30-40 30 35 1050
40-50 25 45 1125
Sum = 100 = n Sum = 3100

Find:
a. The mean.

b. The variance (assume it is a population.)

https://brainmass.com/statistics/probability/probability-mean-variance-standard-deviation-354106

#### Solution Preview

1. Given the following bi variate frequency table

Men Women Totals
Plant worker 280 20 300
Office worker 40 50 90
Field salesman 80 30 110
Totals 400 100 500

a) Probability (Male) = = 0.80
b) Probability (Female) = = 0.20
c) Probability (Plant worker) = = 0.60
d) Probability (Office worker) = = 0.18
e) Probability (Field sales person) = = ...

#### Solution Summary

Probability, mean, variance and standard deviation are discussed.

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