Would it be unusual for the sample mean to be less than 193 ?

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Substituting the given values, we get:

z = (204 - 198) / (39 / √106)

z = 1.58

Using a standard normal distribution table or Excel function, we can find that the probability of a z-score greater than 1.58 is 0.0566.

Therefore, the probability that the sample mean cholesterol level is greater than 204 is:

P(z > 1.32) = 0.0566

(b) To find the probability that the sample mean cholesterol level is between 190 and 197, we can use the same formula and calculate two z-scores:

z1 = (190 - 198) / (39 / √(106))

z1 = -2.06

z2 = (197 - 198) / (39 / √(106))

z2 = -0.32

Using a standard normal distribution table or Excel function, we can find that the probability of a z-score between -2.06 and -0.32 is 0.3789.

Therefore, the probability that the sample mean cholesterol level is between 190 and 197 is:

P(-2.06 < z < -0.32) = 0.3789

(c) To determine whether it would be unusual for the sample mean to be less than 193, we can use the same formula and calculate the z-score:

z = (193 - 198) / (39 / √(106))

z = -1.32

Using a standard normal distribution table or Excel function, we can find that the probability of a z-score less than -1.32 is 0.0934. Since this probability is greater than 0.05, which is often used as a threshold for unusual events, it would not be unusual for the sample mean to be less than 193.

Learn more about probability here:

brainly.com/question/11234923

#SPJ1