The heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm. The heights of all adult females in Croatia are approximately normally distributed with a mean of 158 cm and a standard deviation of 9 cm. If independent random samples of 10 adult males and 10 adult females are taken, what is the probability that the difference in sample means (males – females) is greater than 20 cm?

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michaeleachim122 michaeleachim122 · Answer 1 · 2020-05-07T21:46:17+02:00

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Step-by-step explanation:

.7104

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AFOKE88 AFOKE88 · Answer 2 · 2022-04-26T13:37:50+02:00

The probability that the difference in sample means (males – females) is greater than 20 cm is; 0.7088

The formula for z-score of difference between two means is;

z = (x₁' - x₂' - Δ)/√[(√σ₁²/n₁) + (σ₂²/n₂)]

We are given;

Sample mean 1; x₁' = 180 cm

Sample mean 2; x₂' = 158 cm

Standard deviation 1; σ₁ = 7 cm

Standard Deviation 2; σ₂ = 9 cm

hypothesized difference; Δ = 20 cm

Sample size; n₁ = n₂ = 10

Thus;

z = (180 - 158 - 20)/√[(7²/10) + (9²/10)]

z = 0.55

From online z-score table, we have;

p = 0.71

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