statistics

Question

Janey always waits until her gas tank is nearly empty before she refuel a.   She keeps a record of the distance she drives on each tank of gas.  The distance varies, depending on the weather and the amount she drives on gravel roads .  The distance has a mean of 728 km and a standard deviation of 32 km. 

 

1) what percent of the time did Janey drive between 664 km and 792 km on a tank of gas?

 

2) between which two values will she drive 68% of the time ?

 

A cell phone manufacturer has determined that the phones have a mean life of 63 months with a standard deviation of 9.1 months.  What length of warranty should be offered if the manufacturer wants to repair less than 1% of the phones?

Answer 1

1)

 

Using a z-table:

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

z = (X - μ) / σ, X is score, μ = mean, σ = standard deviation

 

z₆₆₄ = (664 - 728) / 32

z₆₆₄ = -2, 2.28% lie below

 

z₇₉₂ = (792 - 728) / 32

z₇₉₂ = 2, 97.72% lie below

 

97.72% - 2.28%, or 94.44% lie between 664 and 792.

 

Using the normal curve

http://www.regentsprep.org/regents/math/algtrig/ats2/normallesson.htm

 

68% of scores lie between 1 standard deviation below and 1 standard deviation above.

For 68% of the time she drove between 696 and 760.