Answer to Question #311185 in Statistics and Probability for Mitch

Question

Five hundred children participated in a field demonstration. Their heights averaged 110cm with a standard deviation of 6cm.

1. What is the probability that a child picked at random has a height greater than 116cm?

2. What is the probability that the height of a child picked at random is less than 104cm?

3. What is the probability that the height of a child picked at random is between 110cm and 122cm?

4. How many children have heights between 98 and 104cm?

5. How many children belong to the upper 15% of the group?

Answer 1

we use z calculations as below

1.Z(116) = (116 - 110) / 6 = 1

p(x>116) = 1 - p(z<1) , from the normal tables, we have

= 1 - 0.84134 = 0.15866

2.Z(104) = (104 - 110) / 6 = -1

p(x<104) = p(z< -1), from the normal tables, we obtain

= 0.15866

3.z(110) = (110-110)/6 =0

z(122) = (122-110)/6 = 2

p(110<x<122) = p(0<z<2), from the normal tables, we obtain

= (0.97725 - 0.50000) =0.47725

4z(98) = (98-110)/6 = -2

z(104) = (104-110)/6 =-1

p(98<x<104) =p(-2<z<-1) using the normal tables, we obtain

=( 0.15866 - 0.02275) =0.13591

5 from the normal table tables, the z score of the upper 15% is 1.04, so we define

1.04 =(x-110)/6

solving we get x=116.24 which is approximately 117 children