Question

A football player can make a field goal from the 40 yard line 50% of the time. If he makes n = 16 attempts and x = the number of field goals he makes, use a normal curve to approximate the probability distribution for and then use it to determine the approximate probability that I will be greater than or equal to 10.

Answer 1

Given that a football player can make a field goal from the 40 yard line 50% of the time so the population propotrtion would be p = 0.50.

If he makes n = 16 attempts and x = the number of field goals he makes, and alos using a normal curve to approximate the probability distribution so, the probability is calculated using Z score.

So, the approximate probability that he will be greater than or equal to X = 10 is calculated by Z score.

The sample proportion is computed as:

Now the Z score is calculated as:

So, P(X>=10) = P(Z>1) is calculated using excel formula for normal distribution which is =1-NORM.S.DIST(1,TRUE)

Thus the probability is calculated as 0.1587.