Question

mean of 182.5 cm and standard deviation of 10.3. What is the probability that a Dutch male is between 173.5 and 191.5 cm ? Round your answer to three decimal places.

Answer 1

The probability that a Dutch male is between 173.5 and 191.5 cm is 0.616

or 61.6%

Explanation:

Mean = M = 182.5

Standard Deviation = S = 10.3,

We need to find the z values and then calculate the probabilities,

Probability of being lower than 173.5,

P(X < 173.5),

Finding the z value,

z = (x - M)/S

z = (173.5 - 182.5)/10.3

z = -0.87

Then the corresponding value for the area and hence the probability is,

P(X<173.5) = P(z = -0.87) = 0.1922

P(X < 173.5) = 0.1922

Probability of being lower than 191.5,

P(X<191.5)

Finding the z value,

z =(x-M)/S

z = (191.5 - 182.5)/10.3

z = 0.87

Then the corresponding value for the probability is,

P(X < 191.5) = 0.8078

The probability that a Dutch male is between 173.5 and 191.5 cm is,

P(173.5 < X < 191.5) = P(X < 191.5) - P(X < 173.5)

P(173.5 < X < 191.5) = 0.8078 - 0.1922

P(173.5 < X < 191.5) = 0.6156

To 3 decimal places,

P(173.5 < X < 191.5) = 0.616

P(173.5 < X < 191.5) = 61.6%