"I know how to calculate question which are phrased like so A study of data collected at a company manufacturing flashlight batteries shows that a batch of 8000 batteries have a mean life of 250 minutes with a standard deviation of 20 minutes. Assuming a Normal Distribution, estimate: (i) How many batteries will fail before 220 minutes? Answer = 534.4 But I can not figure questions phrased like this: Support call times at a technical support center are Normally distributed with a mean time of 8 minutes and 45 seconds and a standard deviation of 1 minute and 5 seconds. On a particular day, a total of 500 calls are taken at the centre. How many of these calls are likely to last more than 10 minutes I dont understand how to find the z-score in this question as its to do with time?"

sapetih1i

sapetih1i

Open question

2022-08-19

I know how to calculate question which are phrased like so
A study of data collected at a company manufacturing flashlight batteries shows that a batch of 8000 batteries have a mean life of 250 minutes with a standard deviation of 20 minutes. Assuming a Normal Distribution, estimate:
(i) How many batteries will fail before 220 minutes?
Answer = 534.4
But I can not figure questions phrased like this:
Support call times at a technical support center are Normally distributed with a mean time of 8 minutes and 45 seconds and a standard deviation of 1 minute and 5 seconds. On a particular day, a total of 500 calls are taken at the centre. How many of these calls are likely to last more than 10 minutes
I dont understand how to find the z-score in this question as its to do with time?

Answer & Explanation

Brooks Hogan

Brooks Hogan

Beginner2022-08-20Added 18 answers

To calculate the z-score you have to standardize the random variable. The support call time is distributed as T N ( 8.75 , ( 1 1 12 ) 2 )
Reasoning: 45 seconds are 0.75 minutes. And 5 seconds are 1 12 minutes.
Therefore Z = T 8.75 1 1 12 = T 8.75 13 12 . Then it is asked for
P ( T > 10 ) = 1 P ( T 10 ) = 1 Φ ( 10 8.75 13 12 ) = 1 Φ ( 5 4 13 12 ) = 1 Φ ( 15 13 )
This is the probability that one arbitrary call last more than 10 minutes.
Nina Bean

Nina Bean

Beginner2022-08-21Added 3 answers

The Z score is how many standard deviations above the mean 10 minutes is. It is 5/4 minutes more than the mean of eight minutes and forty five seconds, and the standard deviation is 13/12 minutes, so the Z score is 15/13.

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