(Statistics) * Basic probability concepts Hello, would you please answer this qu

Question

(Statistics)

* Basic probability concepts

Hello, would you please answer this question?

I appreciate your help in advance!

3. A production plant produces tires. In a typical week, the number of tires produced is a normally distributed random variable with an average production level of 174 tires (that is, a mean of 174) and a standard deviation of 9 tires. (a.) What is the probability that (or, on how many occasions will) more than 190 tires will be produced by this production plant in any given week? (b.) What is the probability that the plant will produce between 160 and 180 tires in any given week? (c) The manager of the tire plant wants to tell his customers with a 95% probability that produc tion levels will fall within some range, say from xlower to Tupper. What should these values be?

Explanation / Answer

3)

a) probability that more than 190 tires will be produced =

b)

c)

c)

for 95% values fall within 2.5 and 97.5 percentile for which z scores are -/+ 1.96

hence xlower =mean+z*std deviation =174-1.96*9=156.36

xupper =mean+z*std deviation =174+1.96*9=191.64

for normal distribution z score =(X-)/

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