Mathematics, 04.07.2020 02:01 Luena

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).† Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. A. What is the probability that a Dutch male is shorter than 175 cm?
B. What is the probability that a Dutch male is taller than 195 cm?
C. What is the probability that a Dutch male is between 173 and 193 cm?
D. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?

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Answer from: serenityarts123

a) 22.36% probability that a Dutch male is shorter than 175 cm

b) 12.71% probability that a Dutch male is taller than 195 cm

c) 65.78% probability that a Dutch male is between 173 and 193 cm

d) We should expect 251.4 to be taller than 190 cm

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 183, \sigma = 10.5$

A. What is the probability that a Dutch male is shorter than 175 cm?

This is the pvalue of Z when X = 175. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{175 - 183}{10.5}$

Z = -0.76

Z = -0.76 has a pvalue of 0.2236

22.36% probability that a Dutch male is shorter than 175 cm.

B. What is the probability that a Dutch male is taller than 195 cm?

This is 1 subtracted by the pvalue of Z when X = 195. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{195 - 183}{10.5}$

Z = 1.14

Z = 1.14 has a pvalue of 0.8729

1 - 0.8729 = 0.1271

12.71% probability that a Dutch male is taller than 195 cm.

C. What is the probability that a Dutch male is between 173 and 193 cm?

This is the pvalue of Z when X = 193 subtracted by the pvalue of Z when X = 173. So

X = 193

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{193 - 183}{10.5}$

Z = 0.95

Z = 0.95 has a pvalue of 0.8289

X = 173

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{173 - 183}{10.5}$

Z = -0.95

Z = -0.95 has a pvalue of 0.1711

0.8289 - 0.1711 = 0.6578

65.78% probability that a Dutch male is between 173 and 193 cm.

D. Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?

Proportion taller than 190cm is 1 subtracted by the pvalue of Z when X = 190. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{190 - 183}{10.5}$

Z = 0.67

Z = 0.67 has a pvalue of 0.7486

1 - 0.7486 = 0.2514

Out of 1000:

0.2514*1000 = 251.4.

We should expect 251.4 to be taller than 190 cm

Answer from: Quest

answer: on kudzu, being female and being green are independent events.

step-by-step explanation:

Answer from: Quest

Answer is negative 2

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