SOLUTION: A local band is going on a U.S. Summer tour, and they average about 2,000 people per concert, with a standard deviation of about 400. Assume that these concert numbers follow a nor

Question 1120281: A local band is going on a U.S. Summer tour, and they average about 2,000 people per concert, with a standard deviation of about 400. Assume that these concert numbers follow a normal distribution.
a. If a concert is selected at random, what is the probability that there were more than 2,500 people at that concert?
b. If a concert is selected at random, what is the probability that there were less than 1,800 people at that concert?
c. If a concert is selected at random, what is the probability that there were between 1,800 and 2,500 people at that concert?
d. For a concert to be in the top 10% as far as attendance, at least how many people would need to attend the concert?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) Probability (P) ( X > 2500 ) = 1 - P ( X < 2500 )
:
z-score(2500) = (2500 - 2000) / 400 = 1.25
:
look at z-score tables to find probability associated with z-score of 1.25
:
P ( X < 2500 ) = 0.8944
:
P ( X > 2500 ) = 1 - 0.8944 = 0.1056
:
b) z-score(1800) = (1800 - 2000) / 400 = -0.5
:
P ( X < 1800 ) = 0.3085
:
c) P ( 1800 < X < 2500 ) = P ( X < 2500 ) - P ( X <1800 ) = 0.8944 - 0.3085 = 0.5859
:
d) 1 - 0.10 = 0.90
:
z-score for probability 0.90 is 1.28
:
1.28 = (X - 2000) / 400
:
X = (1.28 * 400) + 2000 = 2512
:
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