TRUE OR FALSE
35. A survey of women owned business found that approximately 30% of all small businesses
are owned by non‐Hispanic white women. In a sample of 250 non‐Hispanic businesses
owned by whites, the average number of businesses owned by female would be 75.
36. A shipment of 600 computer chips is received by Bell Computers; the manufacturers of
lap top computers. These chips are supplied by the vendor. The contract specifies that
Bell Computers will accept the shipment only if a sample of 10 chips from the shipment
has at most one defective chip. The probability of accepting the lot can be determined
using a normal probability distribution.
37. The binomial distribution is used to calculate the probability of x number of successes
out of n trials whereas; the Poisson distribution is used to calculate the probability of x
number of occurrences out of n trials.
38. The parameters of Binomial distribution are the number of trials (n) and the probability
of success (p) whereas; the parameter of Poisson distribution is the mean number of
occurrence (m).
39. If the mean number of customer arrivals per unit of time at a bank is 6 then the
probability that no customer will arrive in the that specified time unit can be calculated
using the following expression
60 6 ( 0) .
0!
p x e
40. The misaligned parts in certain type of machine are described as nonconformities. For a
particular type of machine, suppose that the number of nonconformities per machine
follows a Poisson distribution with an average of three nonconformities per machine. In a
quality check, the probability that a quality inspector will find no more than one
nonconformity in the machine is close to 0.1991.
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35. False. To determine whether the statement is true or false, we need to calculate the average number of businesses owned by females in the sample of 250 non-Hispanic businesses owned by whites. However, the question does not provide any information on the percentage of businesses owned by non-Hispanic white women in the overall population. Therefore, we cannot determine the average number of businesses owned by females in the given sample.
36. True. The probability of accepting the lot can be determined using a normal probability distribution if the number of defective chips in a sample of 10 chips follows a normal distribution. However, the question does not provide any information on the distribution or the mean and standard deviation of the number of defective chips in the sample. Therefore, without this information, we cannot determine the probability of accepting the lot using a normal probability distribution.
37. False. The binomial distribution is used to calculate the probability of a fixed number of successes (x) out of a fixed number of trials (n), where the trials are independent and have two possible outcomes (success or failure). On the other hand, the Poisson distribution is used to calculate the probability of a certain number of events (x) occurring in a fixed interval of time or space, where the events occur independently and at a constant average rate (mean). Therefore, the statement is incorrect.
38. True. In the binomial distribution, the parameters are the number of trials (n) and the probability of success (p). The number of trials represents the total number of independent experiments or attempts, while the probability of success represents the probability of a single trial being successful. In the Poisson distribution, the parameter is the mean number of occurrences (m), which represents the average rate at which the events occur. Therefore, the statement is correct.
39. False. The given expression 60 6 ( 0) . 0! p x e - is not a valid expression to calculate the probability that no customer will arrive in a specified time unit, given that the mean number of customer arrivals per unit of time at a bank is 6. The probability of no customer arriving can be calculated using the Poisson distribution formula: P(x = 0) = e^(-λ) where λ is the mean number of occurrences. Therefore, the correct expression should be e^(-6).
40. True. The question states that the number of nonconformities per machine follows a Poisson distribution with an average of three nonconformities per machine. To calculate the probability that a quality inspector will find no more than one nonconformity in the machine, we can use the Poisson distribution formula: P(x ≤ 1) = P(x = 0) + P(x = 1). By substituting the mean number of occurrences (λ = 3) into the formula, we can calculate that the probability is close to 0.1991. Therefore, the statement is true.