Question

please answer and explain both examples

Problem 3. The fares received by taxi drivers working for the Sunshine Cab Company are normally distributed with a mean of $12.50 and a standard deviation of $3.25. Suppose a driver has four independent consecutive fares, and two of those fares are less than $6.00 while two are more. What is the probability of this happening? Problem 4. Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of potato chips that is labeled as 10 ounces should contain at least 10 ounces. Assume that the standard deviation of the packaging equipment yields a bag weight standard deviation of 0.2 ounces. Assume the bag weight distribution is bell-shaped. Determine what average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.

Answer 1

(there are more than 1 different questions, as per policy i am answering first question)

3.

x = fare

P(x<$6) :

The following information has been provided: H =12.5, J = 3.25 We need to compute Pr(X<6). The corresponding z-value needed to be computed: X- Za 6 - 12.5 3.25 2 Therefore, Pr(X < 6) = Prz< 6 - 12.5 3.25 23.-) = Pr(Z < -2) = 0.0228

P(k fares less than 6) = 4Ck * (P(x<$6))^k * (1-P(x<$6))^(4-k)

P(2 fares less than 6) = 4C2 * (0.0228)^2 * (1-0.0228)^(4-2)

= 0.0030 (answer)

(please UPVOTE)