Question

A population of values has a normal distribution with μ = 14.5

and σ = 23 . You intend to draw a random sample of size n = 123 .
Please show your answers as numbers accurate to 4 decimal
places.
Find the probability that a single randomly selected value is greater than 10.8. P(X > 10.8)

Answer 1

To find the probability that a single randomly selected value is greater than 10.8, calculate the z-score using the formula z = (x - μ) / σ and use a standard normal distribution table or calculator to find the corresponding probability. Probability that a single randomly selected value is greater than 10.8 is 0.4373.

Step-by-step explanation:

To find the probability that a single randomly selected value is greater than 10.8, we can use the z-score formula. The z-score represents the number of standard deviations a value is from the mean in a normal distribution. First, we calculate the z-score:

z = (x - μ) / σ

where x is the value we are interested in, μ is the population mean, and σ is the population standard deviation. Plugging in the values, we get:

z = (10.8 - 14.5) / 23 = -0.1609

Next, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score. For a z-score of -0.1609, the probability is approximately 0.4373. Therefore, the probability that a single randomly selected value is greater than 10.8 is approximately 0.4373.