Question

In: Statistics and Probability

Bicycles arrive at a bike shop in boxes. Before they can be​sold, they must be​ unpacked,...

Bicycles arrive at a bike shop in boxes. Before they can be​sold, they must be​ unpacked, assembled, and tuned​(lubricated, adjusted,​ etc.). Based on past​ experience, the shop manager creates a model of how long this may take based on the assumptions that the times for each setup phase are​ independent, each phase follows a Normal​model, and the means and standard deviations of the times in minutes are as shown in the table. Complete parts​ a) and​ b).

Phase Mean SD

Unpacking 3.5 .4

Assembly 22.1 2.8

Tuning 12.5 2.8

a) What are the mean and the standard deviation for the total bicycle setup​ time?

mean=38.1

SD=3.98

​(Round to two decimal places as​ needed.)

​b) A customer decides to buy one of the display models but wants a different color. The shop has​ one, still in the box. The manager says they can have it ready in half an hour. Do you think the bike will be set up and ready to go as​ promised? Explain.

​(Round to four decimal places as​ needed.)

A.​Yes, the probability that the bike will be ready in half an hour is ___________________

B.​No, the probability that the bike will be ready in half an hour is __________________

The quarterly returns for a group of 68 mutual funds are well modeled by a Normal model with a mean of 5.6​% and a standard deviation of 1.6​%. Use the​ 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of​ funds, rather than using technology to find the exact values.

​a) the highest 50​%

​b) the highest 16​%

​c) the lowest 2.5​%

​d) the middle 68​%

Solutions

Expert Solution

orchestra answered 2 years ago
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