I need help with 2 and 5 Use the 68-95-99.7 rule. Draw a picture. Show your work

Question

I need help with 2 and 5

Use the 68-95-99.7 rule. Draw a picture. Show your work. Do not use software for part 1. (5 pts) A certain cell phone’s battery life when new and fully charged is normally distributed with a mean of 14 hours and a standard deviation of one hour.

1. Sketch the normal distribution as shown in class, marking and labelling the values in hours associated with z: {-3,-2,-1,0,1,2,3}

2. What percentage of batteries last between 13-15 hours?

5. If my phone lasts less than 11 hours, what percentile is it in?

Explanation / Answer

Ans:

Mean=14

std dev=1

1)for z=-3

-3=(x-14)/1

x=11

for z=-2

-2=(x-14)/1

x=12

So,corresponding values in hrs will be 11,12,13,14,15,16,17

2)P(13<X<15)

13 and 15 are one standard deviation away from mean.

So,68% of the batteries will last between 13 to 15 hrs.

Note:68-95-99.7 rule

5)P(X<11)

z=(11-14)/1=-3

P(z<-3)=0.0013

It is 0.13%

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