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 1.1-in. In what range would you expect to find the middle 50% of most head breadths

Step-by-step explanation:

Let X the random variable that represent the  head breadths of a population, and for this case we know the distribution for X is given by:

Where and

We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.

We can use the z score formula given by:

The critical values that accumulates 0.25 of the area on each tail we got:

And if we solve x from the z score we got:

And replacing we got: