Question

In a normal distribution with a mean (μ) of 10 and a standard deviation (σ) of 1, what is the probability that a randomly drawn item is either less than 8.5 or greater than 9.5?

A) 0.6247
B) 0.2417
C) 0.7583
D) 0.3413

Answer 1

To find the probability, you can calculate the area under the curve using z-scores.

Step-by-step explanation:

To find the probability that a randomly drawn item is either less than 8.5 or greater than 9.5 in a normal distribution with a mean of 10 and a standard deviation of 1, we can calculate the area under the curve using z-scores. First, we find the z-scores for both values:

Z-score for 8.5: (8.5 - 10) / 1 = -1.5

Z-score for 9.5: (9.5 - 10) / 1 = -0.5

Using a standard normal distribution table or a calculator, we can find the area to the left of -1.5 and the area to the right of -0.5. Then, we add these two areas together to get the probability:

Area to the left of -1.5: 0.0668

Area to the right of -0.5: 0.3085

Probability: 0.0668 + 0.3085 = 0.3753

Therefore, the probability that a randomly drawn item is either less than 8.5 or greater than 9.5 is approximately 0.3753.