Question

The following are questions from a self-quiz.According to some study, the height for Northern European adult males is normally distributed with an average of 181 centimeter and a standard deviation of 7.3 centimeter. Suppose such an adult male is randomly chosen. Let X be height of that person. The next 2 questions correspond to this information. The answer may be rounded up to 3 decimal places of the actual value.a) The probability that the person is between 160 and 170 centimeters isb) The probability that the person is higher than 190 centimeter is

Answer 1

a) 0.064

b) 0.109

Explanation:

We are given the following information in the question:

Mean, μ = 181 centimeter

Standard Deviation, σ = 7.3 centimeter

We are given that the distribution of height for Northern European adult males is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P(person is between 160 and 170 centimeters)

`P(160 \leq x \leq 170) = P(\displaystyle(160 - 181)/(7.3) \leq z \leq \displaystyle(170-181)/(7.3)) = P(-2.8767 \leq z \leq -1.506)\\\\= P(z \leq -1.506) - P(z < -2.8767)\\= 0.066 -0.002 = 0.064 = 6.4\%`

b) P(person is higher than 190 centimeter)

P(x > 190)

`P( x > 190) = P( z > \displaystyle(190 - 181)/(7.3)) = P(z > 1.2328)`

`= 1 - P(z \leq 1.2328)`

Calculation the value from standard normal z table, we have,

`P(x > 190) = 1 - 0.891 = 0.109 = 10.9\%`