Probability and Statistics question?

Question

I figured out part a and C just need help with part B. Thank you

Heights of 10-year-old children are normally distributed with a mean of 52 inches and a standard deviation of 4 inches
a) Find the probability that one randomly selected 10-year-old child is taller than 54 inches

b) Find the probability that two randomly selected 10-year-old children are both taller than 54 inches

c) Find the probability that the mean height of two randomly selected 10-year-old children is greater than 54 inches

Answer 1

Hi,
First, let’s find the probability that a student is taller than 54 inches; then we multiply the two probabilities to get the probability that both will be taller.
If you have a TI-83 Plus or TI-84 calculator, you can find that as follows:
The syntax for this function is normalcdf( lower bound, upper bound, mean, Std. Dev.
a) Press 2nd, DISTR, 2. The term "normalcdf(" will appear on the home screen.
b) Enter 54 for the left boundary, 1E99 for the right boundary, 52 for mean, and 4 for Std Dev.
You will now have normalcdf(54, 1E99, 52, 4 You do not need to close the parentheses,
but it's okay if you do.
c) Press ENTER and .3085 will be displayed.

P(A and B) = P(A)*P(B)
= .3085 * .3085
=.0952 rounded off.

If you don’t have a calculator, I’ll outline how to work this by hand:
1) Calculate the z-value using the formula z = (x - mean)/ Std. Dev.
You should get a z-value of .5
2) You will now need to look in a set of Standard Normal tables to get the value of .1915 for a z-value of .5.
3) Subtract that value, .1915, from .5 (the entire region to the right of the mean.) to get .3085, the area to the right of .5. That’s the same value we got with the calculator.
4) Then use this value in the calculation in step c) above for the calculator.

Hope this helps.

FE

Answer 2

given that you know how to do part a, then
i would think that if the probability of a randomly selected 10 yr old > 54 inches is X, then the probability of 2 randomly sleected childred both taller than 54 inches would be X * X.

Answer 3

b)The probability that ONE child is taller than 54 inches:
Z = (x - µ)/σ = (54 - 52)/4 = 0.5; The probability associated with Z = 0.50 is 0.6915.
0.6915 is the probability that a random child is SHORTER than 54 inches, so the probability that a random child is taller than 54 inches is 1 - 0.6915 = 0.3085. This is the answer you should have gotten for (a), so the probability that 2 randomly selected children are taller than 54 inches is (0.3085)² = 0.0952