1 Engineers must consider the breadths of male heads when designing helmets. The

Question

1

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.1-in and a standard deviation of 0.9-in.

In what range would you expect to find the middle 68% of most head breadths?
Between and .

If you were to draw samples of size 33 from this population, in what range would you expect to find the middle 68% of most averages for the breadths of male heads in the sample?
Between and .

Enter your answers as numbers. Your answers should be accurate to 2 decimal places.

Explanation / Answer

i) middle 68% means that it lies between 1 standard deviations

so z is between -1 and 1

=6.1

=0.9

For z=-1

z=(x-)/

-1 =(x-6.1)/0.9

-1*0.9 =x-6.1

-0.9 =x-6.1

x=6.1-0.9

x=5.2

For z=1

1 =(x-6.1)/0.9

1*0.9 =x-6.1

0.9 =x-6.1

x=6.1+0.9

x=7

So range is between 5.2 and 7

ii)

=6.1

=0.9

s=/n

=0.9/33

=0.1567

For z=-1

x=z*s +

=-1*0.1567 +6.1

=5.94

For z=1

x=z*s +

=1*0.1567 +6.1

=6.26

So,range is between 5.94 and 6.26

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