Question

Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that = np = 30 and = np(1 − p) = 3.4641. approximate the following probabilities using the normal approximation with the continuity correction. (round your answers to four decimal places.)p(x = 24)

A) The probability that x=24
B) The probability that x≤20
C) The probability that x>35
D) The probability that x≥28

Answer 1

To approximate the probabilities, we can use the normal distribution with the continuity correction. A) The probability that x=24 is approximately 0.0606. B) The probability that x≤20 is approximately 0.0062. C) The probability that x>35 is approximately 0.0402. D) The probability that x≥28 is approximately 0.7598.

Step-by-step explanation:

To approximate the probabilities, we can use the normal distribution with the continuity correction. In this case, we use the mean (μ) equal to np, which is 30, and the standard deviation (σ) equal to the square root of np(1-p), which is approximately 3.4641.

A) To calculate the probability that x=24, we can use the normalcdf function with a range of 23.5 to 24.5, using the values of μ and σ. The result is approximately 0.0606.

B) To calculate the probability that x≤20, we can use the normalcdf function with a range of 19.5 to 20.5, using the values of μ and σ. The result is approximately 0.0062.

C) To calculate the probability that x>35, we can subtract the probability that x≤35 from 1. We can use the normalcdf function with a range of 34.5 to 35.5, using the values of μ and σ. The result is approximately 0.0402.

D) To calculate the probability that x≥28, we can subtract the probability that x<28 from 1. We can use the normalcdf function with a range of 27.5 to 28.5, using the values of μ and σ. The result is approximately 0.7598.