company knows that replacement times for the DVD players it produces are Normall

Question

company knows that replacement times for the DVD players it produces are Normally distributed with a mean of 9.7 years and a standard deviation of 2.4 years.

Find the proportion of a randomly selected DVD players that will have a replacement time less than 3.7 years?
P(X < 3.7 years) =

Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 2.3% of the DVD players will be replaced before the warranty expires, what is the time length of the warranty?
warranty =     years

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Explanation / Answer

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    3.7      
u = mean =    9.7      
          
s = standard deviation =    2.4      
          
Thus,          
          
z = (x - u) / s =    -2.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.5   ) =    0.006209665 [ANSWER]

*******************

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.023      
          
Then, using table or technology,          
          
z =    -1.99539331      
          
As x = u + z * s,          
          
where          
          
u = mean =    9.7      
z = the critical z score =    -1.99539331      
s = standard deviation =    2.4      
          
Then          
          
x = critical value =    4.911056056   [ANSWER]

********************************

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.