Question

Let X be normally distributed with mean μ = 24 and standard deviation = 16.

a. Find P(X ≤ 0).
Note: Round your final answer to 4 decimal places.
P(X ≤ 0)
b. Find P(X> 4).
Note: Round your final answer to 4 decimal places.
P(X> 4)
c. Find P4 s X≤ 28).
Note: Round your final answer to 4 decimal places.

Answer 1

To find the probabilities, we need to standardize the values using the Z-score formula:

Z = (X - μ) / σ,

where X is the random variable, μ is the mean, and σ is the standard deviation.

a. P(X ≤ 0):
To find this probability, we need to calculate the Z-score for X = 0 and then find the area to the left of the Z-score.

Z = (0 - 24) / 16 = -1.5.

Using a standard normal distribution table or a calculator, we can find the area to the left of Z = -1.5, which is approximately 0.0668.

Therefore, P(X ≤ 0) ≈ 0.0668.

b. P(X > 4):
To find this probability, we need to calculate the Z-score for X = 4 and find the area to the right of the Z-score.

Z = (4 - 24) / 16 = -1.25.

Using a standard normal distribution table or a calculator, we can find the area to the right of Z = -1.25, which is approximately 0.8944.

Therefore, P(X > 4) ≈ 0.8944.

c. P(X ≤ 28):
To find this probability, we need to calculate the Z-score for X = 28 and find the area to the left of the Z-score.

Z = (28 - 24) / 16 = 0.25.

Using a standard normal distribution table or a calculator, we can find the area to the left of Z = 0.25, which is approximately 0.5987.

Therefore, P(X ≤ 28) ≈ 0.5987.