1 Find the 20th percentile for an aerobics workout that is normally distributed

Question

1 Find the 20th percentile for an aerobics workout that is normally distributed and lasts an average of 60 minutes with a standard deviation of 8 minutes. Explain what this number mean

2

A nutritionist believes the average number of fat grams in one serving of ice cream is 14

grams, with a standard deviation of 3.4 grams. If fat grams in ice cream arenormally distributed and a serving is randomly chosen, what is the probability that its fat content will be more than 7grams?

Is a 7g serving considered unusual?

Explanation / Answer

1) Formula : Z = (X - mean)/std. dev.

P(X <= x) = 0.2
P(Z <= (X - 60)/8) = 0.2
For p = 0.2, z = -0.8416
x = -0.8416*8 + 60 = 53.2672

20% of the aerobics workout data lies below this value

2) P(X > 7) = 1 - P(Z < (7-14)/3.4) = 1 - P(Z < -2.0588) = 1 - 0.01976 = 0.98024

yes 7 g is unusual as it lies below 5 percentile

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