statistic

1. A production manager knows that 5% of components produced by a particular manufacturing process have some defect. Six of these components, whose characteristics can be assumed to be independent of each other, are examined.

a. (5 pts.) What is the probability that none of these components have a defect?

b. (5 pts.) What is the probability that one of these components has a defect?

c. (10 pts.) What is the probability that at least two of these components have a defect?

d. (10 pts.) What is the expected value for the non-defected ones?

e. (10 pts.) What is the standard deviation of these components has a defect?

2. The number of accidents in a production facility has a mean of 2.6 per month.

a.  (5 pts.) For a given month what is the probability there will be fewer than 2 accidents?

b.  (10 pts.) For a given 2 months what is the probability there will be more than 3 accidents?

c.  (5 pts.) What is the standard deviation for four months period?

3. Forest Green Brown, Inc., produces bags of cypress mulch. The weight in pounds per bag varies, as indicated in the accompanying table.

Weight in pounds	44	45	46	47	48	49	50
Proportion of bags	0.04	0.13	0.21	0.29	0.20	0.10	0.03

a. (10 pts.) What is the probability that a randomly selected chosen bag will contain more that 45 and less than 49 pounds of mulch (inclusive)?

b. (10 pts.) Compute the mean and the standard deviation of the weight of the weight per bag.

c. (10 pts.) The cost (in cents) of producing a bag of mulch is 75+2X, where X is the number of pounds per bag. The revenue from selling the bag regardless of weight, is $250. If profit is defined as the difference between revenue and cost, find the mean and standard deviation of profit per bag. (Hint:𝐸(𝑎𝑋+𝑏)=𝑎𝐸(𝑋)+𝑏; 𝑉(𝑎𝑋+𝑏)=𝑎2𝑉(𝑋))

d. (10 pts.) Two packages are chosen at random. What is the probability that at least one of them contains at least 47 pounds?