The opera theater manager assumes that 10% of the opera tickets for tonight's show have been sold. If the manager is right, what is the probability that the proportion of tickets sold in a sample of 429 tickets would be less than 6%? Round your answer to four decimal places.
The opera theater manager assumes that 10% of the opera tickets for tonight's show have been sold.
If the manager is right, what is the
Let X denotes tickets being sold.
Probability of a ticket being sold (p) is given to be 0.1.
a sample size (n) of 429 tickets is considered.
To calculate the chances that less than 6% of tickets would be sold.
6% of 429=25.7426
To calculate P[X<26].
Here X follows a binomial distribution. A ticket will have 2 outcomes- either it is sold or not.
mean of distribution = np = 429x0.1 = 42.9
variance of distribution = np(1-p) = 38.61
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