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 compary reseatchers have determined that the population of potential clientele have head breadths that are nomally distributed with a mean of 7 1 in and a standard deviation of 0.8-in in what range would you expect to find the middle 95% of most head breadth? Between and f you were to draw samples of ssze 32 tom tas population. tn what range would you expect to find the middle 95% of most averages for the breadths of male heads as the sample? Between and Enter your answers as numbers. Your answers should be accurate to 2 decimal places

Explanation / Answer

as for middle 95% values crtical z =1.96

a)middle 95% values =mean -/+z*std deviaiton =7.1-/+1.96*0.8=5.53 to 8.67

b)for sample size n=32

middle 95% values =mean -/+z*std deviaiton/sqrt(n) =7.1-/+1.96*0.8/sqrt(32)=6.82 and 7.38

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