Mathematics, 13.08.2020 23:01 davidb1113

The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches. A sample of 50 men and 40 women is selected. What is the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights

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The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

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

Z = $\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }$ ~ N(0,1)

where, $\mu_M$ = population mean height of men at UMBC = 69 inches

$\mu_W$ = population mean height of women at UMBC = 65 inches

$\sigma_M$ = standard deviation of men at UMBC = 4 inches

$\sigma_M$ = standard deviation of women at UMBC = 3 inches

n_M = sample of men = 50

n_W = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P( $\bar X_M-\bar X_W$ > 5 inches)

P( $\bar X_M-\bar X_W$ > 5 inches) = P( $\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }$ > $\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }$ ) = P(Z > 1.35)

= 1 - P(Z $\leq$ 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.

Answer from: Quest

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

Answer from: Quest

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!

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The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches....