Mathematics, 27.02.2020 02:06 mccdp55

The heights of women aged 20 to 29 are approximately Normal with mean 61 inches and standard deviation 2.5 inches. Men the same age have mean height 71 inches with standard deviation 2.6 inches. (a) What is the z-score for a woman who is 6 feet tall? Please use 2 decimal places. (b) What is the z-score for a man who is 6 feet tall? Please use 2 decimal places. (c) Who is relatively taller? They are the same relative height. It is impossible to answer this question using the information given. The woman is relatively taller. The man is relatively taller.

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Answer from: rallen1158

a) Z = 4.4

b) Z = 0.38

c) The woman is relatively taller.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

a) What is the z-score for a woman who is 6 feet tall? Please use 2 decimal places.

The heights of women aged 20 to 29 are approximately Normal with mean 61 inches and standard deviation 2.5 inches, which means that $\mu = 61, \sigma = 2.5$ .

The mean and the standard deviation are in inches, so X is also must be in inches. Each feet has 12 inches. So X = 6*12 = 72 inches.

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

$Z = \frac{72 - 61}{2.5}$

Z = 4.4

(b) What is the z-score for a man who is 6 feet tall? Please use 2 decimal places.

Men the same age have mean height 71 inches with standard deviation 2.6 inches, which means that $\mu = 71, \sigma = 2.6$

The mean and the standard deviation are in inches, so X is also must be in inches. Each feet has 12 inches. So X = 6*12 = 72 inches.

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

$Z = \frac{72 - 71}{2.6}$

Z = 0.38

The woman has the higher z-score, so she is relatively taller.

Answer from: Quest

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =) take the ln of both sides

ln (1/2) = ) and we can write

ln(1/2) = ) lne and lne = 1 so we have

ln(1/2) = -.1092t divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

Answer from: Quest

It is 2 out of 8 she will pick green and 3 out of 7 she will pick green but red and green would be 5 out of 5 so 50% chance

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