Question

PROBLEM 1 It is well known that adult male heights follow a normal (Gaussian) distribution. The same is true of adult female heights. For general Canadian population in the range from 18 to 79 years of age, male height follows N(175 cm;7.5 cm), while female height follows N(162 cm; 7.5 cm). Depending on your gender, determine the following: I am (select one): O FEMALE MALE A. Make a (rough) sketch of the distribution, label it indicating the mean and your height What percentile of the population is your height corresponding to? Hint: area under the curve to the left of your height is corresponding to the percentile value you want to find. B. If a random sample of 12 students is selected, what is the probability that the mean of their height is below the gender-specific population average? C. Find a probability that a student of the same gender randomly selected from the class is taller than you. D.

Answer 1

The summary statistics of male and female heights are as follows: Male N(175cm, 7.5cm) Female~ N(162cm, 7.5cm) Let us assume a male with 173 cm. Then, The sketch of the distribution is, Distribution Plot Normal, Mean 175, StDev 2.74 0.16 0.14 0.12 0.10 0.08 0.06 0.02 0.00 173 175 The percentile of the population the male height corresponding to is, (x-u< 173-175 P(XS 173)-P 7.5 2.74 P(zs-0.73) -0.2327 23.27%

For a random sample of 12 students, the probability that the mean of their heights is below the corresponding male height is, X- 173-175 P(X s173)-P 0.79 P(zS-2.53) = 0.0057 0.57%) The probability that a male student randomly selected from the class is taller than the corresponding male is, X-μ 173-175 2.74 P(z>-0.73) = 1-P(25-0.73) 1-0.2327 = 0.7673 [76.73%)