X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 10.33. (Note: the diagram is not necessarily to scale.)
A) 7.1
B) 8.7
C) 9.0
D) 10.2

Question

X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 10.33. (Note: the diagram is not necessarily to scale.) 
A) 7.1 
B) 8.7 
C) 9.0 
D) 10.2

Quizplus · Accepted Answer

Since X is normally distributed, we can use the standard normal distribution to find the value that corresponds to the 64.8th percentile. Using a z-table or calculator, we find that this value is approximately 0.41.

We can then use the formula:
z = (x - μ) / σ

Where μ is the mean of X and σ is the standard deviation of X.

Plugging in the given values, we have:
0.41 = (10.33 - μ) / 3.50

Solving for μ, we get:
μ = 10.33 - (0.41 * 3.50) ≈ 9.0

Therefore, the mean of X is approximately 9.0, which corresponds to choice C.

X Is a Normally Distributed Random Variable with a Standard