Question

Assume the random variable X is normally distributed with mean = 50 and standard deviation o=7. Compute the

probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.
P(X>35)

Answer 1

The probability that a normally distributed random variable X with mean 50 and standard deviation 7 is greater than 35 is approximately 1.66%.

Step-by-step explanation:

The student has asked to compute the probability P(X>35) for a normally distributed random variable X with a mean of 50 and a standard deviation of 7. To find this probability, we can use a standard normal distribution table, a calculator, or statistical software that can compute probabilities for normal distributions.

First, we need to convert the random variable X to the standard normal variable Z:

Z = (X - mean) / standard deviation

Z = (35 - 50) / 7 = -15 / 7 ≈ -2.14

Now we find P(Z > -2.14). The standard normal distribution is symmetric about the mean (which is 0 for Z), so we can calculate P(Z < 2.14) and subtract this from 1 to get the desired probability:

P(X>35) = 1 - P(Z < 2.14)

Using a Z-table or calculator, we find that P(Z < 2.14) is approximately 0.9834. Therefore,

P(X>35) ≈ 1 - 0.9834 = 0.0166

The probability that X is greater than 35 is approximately 1.66%.