1.) Let x be a random variable that represents the length of time it takes a stu
ID: 3358747 • Letter: 1
Question
1.) Let x be a random variable that represents the length of time it takes a student to complete a Science Fair project. From long term experience, it is known that x has a normal distribution with a mean of 3.6 hours anda standard deviation of 0.5 hours. Convert each of the following x intervals into standard z intervals. a.) x24.5 b.) x2.5 D&S; Find the following: 3.be.. .½ .3.4. : o.g d.) P(x 2 4.5) e.) PO 2.24) #249-ese 2 45-14):1-0.9 641 0.035 2.) The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with a mean of 6.7 minutes and a standard deviation of 2.2 minutes. For a door selected at random, what is the probability that the time it takes to assemble will be: a.) 5 minutes or less? b.) 10 minutes or more? c.) Between 5 and 10 minutes? d.) What is the maximum amount of time it takes to complete a door assembly when considering only the fastest 10% of assembly times? 3.) From long term experience, it is known that the time it takes to do an oil change on a vehicle has a normal distribution with a mean of 17.8 minutes and a standard deviation of 5.2 minutes. An auto service shop will give a free oil change to any customer who has to wait longer than the guaranteed time it takes to complete the job. a.) If the shop guarantees the service will take 25 minutes or less, what percentage of customers will end up receiving a free oil change? b ) If the shop does not want to give more than 1% of its customers a free oil change, how long should the guarantee be for? Cround answer to the nearest minuteExplanation / Answer
2) Mean = 6.7
Stdev = 2.2
a. P(X<5) = P(Z< (5-6.7)/2.2) =P(Z<-.773) = .22
b. P(X>=10) = P(Z>= (10-6.7)/2.2) = P(Z>=1.5) = .0668
c. P(5<X<10) = P(X=10) - P(X=5) = (1-P(X>=10)) - P(X=5) = .9332-.22 = .7132
d. P(X<=c) = .10
(c-6.7)/2.2 = 1.28
c = 1.28*2.2+6.7 = 9.516
So, max amount of time it takes to complete a door assembly when considering only the
fastest 10% of assembly time is 9.516
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