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

Question

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 6.2-in and a standard deviation of 1.1-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

mean=6.2

sd=1.1

u expect to find the middle 68% of most head breadths lies in between

mean-sd and mean+sd

6.2-1.1 and 6.2+1.1

5.1 and 7.3

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 .

sample size=n=33

mean-sd/sqrt(n) and mean+sd/sqrt(n)

6.2-1.1/(sqrt(33) and 6.2+1.1/sqrt(33)

6.2 -0.1914854 and 6.2+0.1914854

6.008515 and  6.391485

6.01 and 6.39

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