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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 5.9 inches and a standard deviation of 0.8 inches.

According to the 68-95-99.7 rule, we expect 95% of head breadths to be
between blank and blank inches.

Respuesta :

Answer:

We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 5.9 inches, standard deviation = 0.8 inches.

We expect 95% of head breadths to be between

Within 2 standard deviations of the mean, so:

5.9 - 2*0.8 = 5.9 - 1.6 = 4.3 inches

5.9 + 2*0.8 = 5.9 + 1.6 = 7.5 inches

We expect 95% of head breadths to be between 4.3 inches and 7.5 inches.

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