HELP ANSWER NORMAL APPROXIMATION QUESTION ASAP

Question

After a tough Data Management exam, Jacob decides to visit an amusement park and play the ring-toss game. He was told that the probability of winning a large stuffed animal on each toss is about 33% and he has just enough money to play this game exactly 20 times.

Calculate the probability that he will win exactly 7 stuffed animals using the Normal Approximation method. Show all your work.

Answer 1

To get the P(7), we get the probability that x is between 6.5 and 7.5, or p-hat is between

6.5/20 = .0325 and

7.5/20 = .0375

SE = sqrt(.33*(1-.33)/20)

Then,P(7) = P((.325-.33)/(sqrt(.33*(1-.33)/20)) <= z <= P((.375-.33)/(sqrt(.33*(1-.33)/20))) =

Φ(0.427989525480826) - Φ(-0.0475543917200918) = , i n Excel,

norm.s.dist(0.427989525480826,1) - norm.s.dist(-0.0475543917200918,1) =

0.184634936296571 By the way, the ,1 says that we are using the cumulative probability, not the density.

The actual probability is, again using Excel, binom.dist(7,20,.33,0) = 0.181127243698391

Note that we switched to the ,0, as we have exactly 7.

The normal approximation is 0.184634936296571

The exact probability is 0.181127243698391