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Statistics: Calculate probabilities in contingency tables

1. Refer to the contingency table below and calculate the following probabilities.
Smoker Nonsmoker Row Total
(S) (N)
White (W) 290 560 850
Black (B) 30 120 150
Column Total 320 680 1000
a) P(S)

b) P(W)

c) P(S | W)

d) P(S | B)

e) P(S and W)

2. Bob sets two alarm clocks (battery-powered) to be sure he arises for his Monday 8:00 A.M. accounting exam. There is a 75 percent chance that either clock will wake Bob. What is the probability that Bob will oversleep? (2 pts)

3. Although television HDTV converters are tested before they are placed in the installer's truck, the installer knows that 20 percent of them still won't work properly. The driver must install eight converters today in an apartment building.
a) Ten converters are placed in the truck. What is the probability that the driver will have more than enough working converters? (Round your answer to 4 decimal places.) (2pts)

b) How many boxes should the driver load to ensure a 95 percent probability of having more than enough working converters? (2pts)

4. There is a 14 percent chance that a Noodles & Company customer will order bread with the meal. Find the probability that in a sample of 10 customers
a) More than five will order bread. (Round your answer to 4 decimal places.) (2pts)

b) No more than two will. (Round your answer to 4 decimal places.) (2pts)

c) None of the 10 will order bread. (Round your answer to 4 decimal places.) (2pts)

Solution Preview

Please find solutions/explanations attached herewith.

1. Refer to the contingency table below and calculate the following probabilities. (1 pt each)
Smoker Nonsmoker Row Total
(S) (N)
White (W) 290 560 850
Black (B) 30 120 150
Column Total 320 680 1000
a) P(S)

P(S) = 320/1000 = 0.32

b) P(W)

P(W) = 850/1000 = 0.85

c) P(S | W)

P(S|W) = P(S ∩ W)/P(W) = (290/1000)/(850/1000) = 29/85 = 0.341

d) P(S | B)

P(S|B) = P(S ∩ B)/P(B) = (30/1000)/(150/1000) = 30/150 = 0.2

e) P(S and W)

P(S and W) = 290/1000 = 0.29

2. Bob sets two alarm clocks (battery-powered) to be sure he arises for his ...

Solution Summary

The expert calculates probabilities in contingency tables.

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