Let the random variable X follow a normal distribution with mu equals 40 and sigma 2 equals 49. a. Find the probability that X is greater than 50. b. Find the probability that X is greater than 25 and less than 52. c. Find the probability that X is less than 45. d. The probability is 0.1 that X is greater than what number? e. The probability is 0.07 that X is in the symmetric interval about the mean between which two numbers?
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Given: - \( \mu = 40 \) - \( \sigma = 7 \) (since \( \sigma^2 = 49 \)) We will use the standard normal distribution \( Z \) to find the probabilities. The standard normal variable \( Z \) is given by: \[ Z = \frac{X - \mu}{\sigma} \] ### Part (a): Find the Show more…
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