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Answer:
(a) The probability that the number of successes is at most 5 is 0.1379.
(b) The probability that the number of successes is at most 5 is 0.1379.
(c) The probability that the number of successes is at most 5 is 0.1379.
(d) The probability that the number of successes is at most 11 is 0.9357.
→ All the exact probabilities are more than the approximated probability.
Step-by-step explanation:
Let <em>S</em> = a basketball player scores a shot.
The probability that a basketball player scores a shot is, P (S) = <em>p</em> = 0.30.
The number of sample selected is, <em>n</em> = 25.
The random variable
According to the central limit theorem if the sample taken from an unknown population is large then the sampling distribution of the sample proportion () follows a normal distribution.
The mean of the the sampling distribution of the sample proportion is:
The standard deviation of the the sampling distribution of the sample proportion is:
(a)
Compute the probability that the number of successes is at most 5 as follows:
The probability of 5 successes is:
**Use the standard normal table for probability.
Thus, the probability that the number of successes is at most 5 is 0.1379.
The exact probability that the number of successes is at most 5 is:
The exact probability is more than the approximated probability.
(b)
Compute the probability that the number of successes is at most 7 as follows:
The probability of 5 successes is:
**Use the standard normal table for probability.
Thus, the probability that the number of successes is at most 7 is 0.4129.
The exact probability that the number of successes is at most 7 is:
The exact probability is more than the approximated probability.
(c)
Compute the probability that the number of successes is at most 9 as follows:
The probability of 5 successes is:
**Use the standard normal table for probability.
Thus, the probability that the number of successes is at most 9 is 0.7422.
The exact probability that the number of successes is at most 9 is:
The exact probability is more than the approximated probability.
(d)
Compute the probability that the number of successes is at most 11 as follows:
The probability of 5 successes is:
**Use the standard normal table for probability.
Thus, the probability that the number of successes is at most 11 is 0.9357.
The exact probability that the number of successes is at most 11 is:
The exact probability is more than the approximated probability.
