Suppose that 19% of all sales are for amounts greater than $1,000.In a random sample of 30 invoices,what is the probability that more than six of the invoices are for over $1,000? Use the binomial approximation for the normal distribution.
A)0.4443
B)0.9440
C)0.5557
D)0.0560

Question

Quizplus · Accepted Answer

The probability of an invoice being for over $1,000 is 0.19. The probability of an invoice being for $1,000 or less is 0.81. The mean of the binomial distribution is np = 30 * 0.19 = 5.7. The standard deviation of the binomial distribution is sqrt(np(1-p)) = sqrt(30 * 0.19 * 0.81) = 2.39. The probability of more than six of the invoices being for over $1,000 is the probability of getting more than 6 successes in 30 trials, which is the area under the normal distribution curve to the right of 6.5 (since 6.5 is the midpoint between 6 and 7). This area is 0.4443.

Suppose That 19% of All Sales Are for Amounts Greater