Question

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 is

b) The probability that the person is higher than 190 centimeter is

Please state how you determined the probability from the standard normal table.

Answer 1

Answer:

0.0635,0.1093

Step-by-step explanation:

Given that 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.

X is N*(171,7.3)

a) The probability that the person is between 160 and 170 centimeters is

=$P(160<x<170)\\= P(\frac{160-181}{7.3} <Z<\frac{170-181}{7.3})\\=P(-2.88<z<-1.51)$

Take any std normal table where prob are given from 0 to 3

Since symmetrical we take the prob for 1.51 and 2.88 and find the difference

= 0.4980-0.4345

=0.0635

b) The probability that the person is higher than 190 centimeter is

=$P(X>190)\\= P(Z>1.23)$

= 0.5-value corresponding to 1.23

= 0.5-0.3907

=0.1093