Mathematics: If allison has twelve female cousins and fifteen male cousins , what fraction of her cousins is male

If allison has twelve female cousins and fifteen

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24.03.2023

a) 0.5

b) 0.309

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 70 inches

Standard Deviation, σ = 4 inches

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Height of George Washington = 6 feet = $6\times 12 = 72\text{ inches}$

x = 72

a) z-score

$z_{score} = \displaystyle\frac{72-70}{4} = 0.5$

Interpretation:

This, mean that George Washington is 0.5 standard deviation more than the mean height of for men.

b) P(individual will be as tall or taller than George Washington)

$P( x \geq 72) = P( z \geq 0.5)$

= 1 - P(z < 0.5)

Calculation the value from standard normal z table, we have,

$P(x \geq 72) = 1 - 0.691 = 0.309 = 30.9\%$

Interpretation:

0.309 is the probability that a randomly selected individual will be as tall or taller than George Washington.

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