Question

Assume the random variable X is normally distributed with mean. μ=50 and σ=7.Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Answer 1

To find the probability that the sample mean is between 42 and 50, we use the normal distribution with a mean of 50 and a standard deviation of 7. By finding the difference between the cumulative probabilities for the z-scores corresponding to 42 and 50, we can calculate the desired probability.

Step-by-step explanation:

The probability of a sample mean being between two values can be calculated using the normal distribution.

In this case, we have a normal distribution with a mean of 50 and a standard deviation of 7. To find the probability that the sample mean is between 42 and 50, we need to find the corresponding area under the normal curve.

Using a z-score table or a statistical software, we can find that the z-score for 42 is approximately -1.43 and the z-score for 50 is 0.

The probability can be calculated by finding the difference between the cumulative probabilities for these two z-scores. We can calculate this using the formula:

P(42 < X < 50) = P(X < 50) - P(X < 42).

Using the z-score table or a statistical software, we can find the corresponding cumulative probabilities and subtract them to find the desired probability.