Question

q1.

A manufacturer knows that their items have a normally distributed length, with a mean of 15 inches, and standard deviation of 3.4 inches.

If one item is chosen at random, what is the probability that it is less than 11.5 inches long?

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q2.

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 62 and a standard deviation of 9. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 62 and 71? Do not enter the percent symbol. ans = %

q3. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 62 months and a standard deviation of 6 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 44 and 50 months? Do not enter the percent symbol. ans = %

q4. The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 41 and a standard deviation of 11. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 30 and 74? Do not enter the percent symbol. ans = %

Answer 1

q1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	15
std deviation   =σ=	3.400

probability that it is less than 11.5 inches long:

probability =

P(X<11.5)

=

P(Z<-1.03)=

0.1515

2)

for 62 is at mean and 71 is one standard deviation above mean:

approximate percentage of lightbulb replacement requests numbering between 62 and 71 =34.0 %

3)

for 44 and 50 months are 2 and 3 standard deviation below mean:

approximate percentage of cars that remain in service between 44 and 50 months =(2.5-0.15) =2.35 %

4)

30 and 74 are 1 standard deviaiton below and 3 standard deviation above from mean

approximate percentage of 1-mile long roadways with potholes numbering between 30 and 74 =99.85-16 =83.85 %