5. Race Times : A local medical research association proposes to sponsor a footr

Question

5. Race Times: A local medical research association proposes to sponsor a footrace. The average time it takes to run the course is 45.8 minutes with a standard deviation of 3.6 minutes. Assume that the variable is normally distributed. If the association decides to include only the top 20% of the racers, answer the following questions:

a) What should be the cutoff time in the tryout run?   

b) Would a person who runs the course in 40 minutes qualify? Justify your answer.

6. Wristwatch Lifetimes. The mean lifetime of a wristwatch is 25 months, with a standard deviation of 5 months. If the distribution is normal, for how many months should a guarantee be made if the manufacturer does not want to exchange more than 10% of the watches?

Explanation / Answer

5.

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.2      
          
Then, using table or technology,          
          
z =    -0.841621234      
          
As x = u + z * s,          
          
where          
          
u = mean =    45.8      
z = the critical z score =    -0.841621234      
s = standard deviation =    3.6      
          
Then          
          
x = critical value =    42.77016356   [ANSWER]

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b)

As 40 minutes is below the qualifying time of 42.77 minutes in part a, then YES, HE QUALIFIES. [ANSWER]

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