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Two companies market new batteries targeted at owners of personal music players. Dura Tunes claims a...

  1. Two companies market new batteries targeted at owners of personal music players. Dura Tunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours.

a. Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy.

b. Suppose the standard deviations are 2 hours for DuraTunes and 1.5 hours for RockReady. You are headed for 8 hours at the beach. Which battery is most likely to last all day? Explain.

PLEASE SHOW ALL WORK AND RATIONALE.

TYPED WORK ONLY PLEASE

NO HANDWRITTEN.

Solutions

Expert Solution

(A) We would like to know the standard deviations of the battery lifespans before deciding which brand to buy because standard deviation helps us in knowing the minimum and maximum battery life depending upon the different possible situations. So, it is important to know the standard deviation of the battery lifespans. Standard deviation will tells us which battery is more relaible for work and which is not reliable because small standard deviation provides higher reliability and higher standard deviation provides lower reliability.

(B) Mean battery life for Dura Tunes is 11 hours and RockReady is 12 hours

Assuming normal distribution

we can say that 95% of data the will fall within 2 standard deviation from the mean

standard deviation for Dura Tunes is 2 hours and 2 hours for RockReady

Calculation for DuraTune

Calculation for RockReady

So, it is clear that 95% of times DuraTune will last between 7 hours to 15 hours whereas RockReady will last between 9 hours to 15 hours

We need battery supply for at least 8 hours, So it is clear that RockReady is more reliable and it can give better battery life performance as compared to DuraTune.

milcah answered 1 year ago
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