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.

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.

a

step-by-step explanation:

jjddbdhid r

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.