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 6.4-in and a standard deviation of 0.9-in. In what range would you expect to find the middle 50% of most head breadths? Between and . If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 50% 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.

Complete 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 6.4-in and a standard deviation of 0.9-in.If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 50% of most averages for the breadths of male heads in the sample

The range is  from    to  

Step-by-step explanation:

From the question we are told that

   The mean is  

   The standard deviation  

    The sample  size is  n  =  47  

Generally the standard error is mathematically represented as

=>            

Generally the proportion where the middle 50% of most average for the breaths of male heads in the sample is mathematically evaluated as

Generally  

So

From the z table  the z-score of  0.5 is

So

and

step-by-step explanation:

through just a quick inspection, one can see that the graph of this cubing function starts in quadrant iii and ends in quadrant i.   when x = 0, y = 3, so the y-intercept is (0, 3).

if graphs are part of the problem statement, share them.   .