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 6.7-in and a standard deviation of 1.2-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 43 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.

Answer 1

Solution:

Given in the question

Population mean = 6.7

Standard deviation = 1.2

According to the empirical rule middle 68% of most values are +/- 1 standard deviation of mean so

Lower bound = 6.7-1.2 = 5.5

Upper bound = 6.7+1.2 = 7.9

So 68% of most head breadth are in between 5.5 and 7.9

Solution(b)

Test critical value can be calculated as Df = 42, t-value = 1.01

So lower bound = 6.7-1.2*1.01 = 6.7- 1.21 = 5.49

Upper bound = 6.7+1.2*1.01 = 6.7+1.21 = 7.91

So if you draw sample of size 43, than range 5.49 to 7.91 would be expect middle 68% of the most averages.