Mathematics, 24.06.2020 17:01 brandonshaw16

In a survey of women in a certain country (ages 20 minus29), the mean height was 66.2 inches with a standard deviation of 2.86 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (round to two decimal places as needed) (b) What height represents the first quartile? (round to two decimal places as needed.)

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Answer from: hanjonez

(a) The height of 70.90 inches represents the 95th percentile.

(b) The height of 64.27 inches represents the first quartile.

Step-by-step explanation:

We are given that in a survey of women in a certain country (ages 20-29), the mean height was 66.2 inches with a standard deviation of 2.86 inches.

Let X = heights of women in a certain country.

So, X ~ Normal( $\mu=66.2,\sigma^{2} =2.86^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean height = 66.2 inches

$\sigma$ = standard deviation = 2.86 inches

(a) We have to find the height that represents 95th percentile, that means;

P(X < x) = 0.95 {wherex is the required height}

P( $\frac{X-\mu}{\sigma}$ < $\frac{x-66.2}{2.86}$ ) = 0.95

P(Z < $\frac{x-66.2}{2.86}$ ) = 0.95

Now, in the z table the critical value of x that represents the top 5% area is given by 1.645, that is;

$\frac{x-66.2}{2.86}=1.645$

${x-66.2=1.645\times 2.86$

x = 66.2 + 4.70 = 70.90 inches

So, the height of 70.90 inches represents the 95th percentile.

(b) We have to find the height that represents the first quartile, that means;

P(X < x) = 0.25 {wherex is the required height}

P( $\frac{X-\mu}{\sigma}$ < $\frac{x-66.2}{2.86}$ ) = 0.25

P(Z < $\frac{x-66.2}{2.86}$ ) = 0.25

Now, in the z table the critical value of x that represents the below 25% area is given by -0.6745, that is;

$\frac{x-66.2}{2.86}=-0.6745$

${x-66.2=-0.6745\times 2.86$

x = 66.2 - 1.93 = 64.27 inches

So, the height of 64.27 inches represents the first quartile.

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

so then what are you asking?

step-by-step explanation:

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In a survey of women in a certain country (ages 20 minus29), the mean height was 66.2 inches with a...