Question

The height of adult males follows approximately a normal distribution with µ = 178 cm and σ = 7 cm. Suppose we have an i.i.d. sample of n = 20 elements from this population.

a) Find the probability that the height of a particular male is between 174 cm and 180 cm.

b) Find the probability that the sample mean lies between 174 cm and 180

cm.

Answer 1

This is a normal distribution question with

a)

P(174.0 < x < 180.0)=?

This implies that

P(174.0 < x < 180.0) = P(-0.5714 < z < 0.2857) = P(Z < 0.2857) - P(Z < -0.5714)

P(174.0 < x < 180.0) = 0.6124460476514143 - 0.2838642645473

b) Sample size (n) = 20

Since we know that

P(174.0 < x < 180.0)=?

This implies that

P(174.0 < x < 180.0) = P(-2.5556 < z < 1.2778) = P(Z < 1.2778) - P(Z < -2.5556)

P(174.0 < x < 180.0) = 0.8993400227949766 - 0.00530024485427263

PS: you have to refer z score table to find the final probabilities.

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