Statistics and Z

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

𝜇 = 15.2; 𝜎 = 3.9

P(10 ≤ x ≤ 26) =  

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

𝜇 = 13.8; 𝜎 = 2.8

P(8 ≤ x ≤ 12) =  

Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.4 months and a standard deviation of 8.1 months.

(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)

 %

(b) If Quick Start does not want to make refunds for more than 5% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

 months

  

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.1 minutes and a standard deviation of 3.3minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.

(a) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

 

(b) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

 

(c) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

 

(a) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

 

(b) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

 

(c) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

(a) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)

 

(b) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)

 

(c) What is the probability that for 39 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

Answer 1

1a - using SALT. P = .9060 using the SALT link, this is child's play.

Try it, it's fun!

The jet problem is poorly stated. Making some assumptions we can restate the question.

2a)

If the mean taxi/take off time for a population of planes is 8.1 min with a sd of 3.3min what is the probabilityt that out of a sample of 39 that the average t/t time for the 39 flights would be less then or equal to 8.209 min (320/39)? Since this is a question about means we use the standard deviation of the mean which would be 3.3/√39 or 0.528. using SALT. P(mu < 8.209) = 0.5818

The rest of the questions are answered similarly.