Question

A Normal Distribution has mean = 80 and standard deviation = 12. The probability of selecting a value between 70 and 85 is:

A) 0.4595
B) 0.8944
C) 0.6911
D) 0.95

Answer 1

The probability of selecting a value between 70 and 85 in a normal distribution with a mean of 80 and a standard deviation of 12 is approximately 0.4595.

Step-by-step explanation:

To find the probability of selecting a value between 70 and 85 in a normal distribution with a mean of 80 and a standard deviation of 12, we need to find the area under the curve between these two values.

First, we find the z-scores for both 70 and 85: z1 = (70 - 80) / 12 = -0.83 and z2

= (85 - 80) / 12

= 0.42.

Using a standard normal distribution table or calculator, we can find the area to the left of z1 and subtract it from the area to the left of z2: P(70 <= X <= 85) = P(-0.83 <= Z <= 0.42) = P(Z <= 0.42) - P(Z <= -0.83) = 0.6631 - 0.2033

= 0.4598.

Therefore, the correct answer is A) 0.4595.