Question

a) find the area above 66 for a n(60,10) distribution b) find the area below 48 for a n(60,10) distribution.

Answer 1

To find the area above 66 for a normal distribution with a mean of 60 and a standard deviation of 10 (N(60,10)), calculate the probability that a value is greater than 66. To find the area below 48, calculate the probability that a value is less than 48.

Step-by-step explanation:

To find the area above 66 for a normal distribution with a mean of 60 and a standard deviation of 10 (N(60,10)), we need to calculate the probability that a value is greater than 66.

Using a standard normal distribution table or a calculator, we can find the z-score for 66: z = (66 - 60) / 10 = 0.6

The area above 66 is equal to the area to the right of 0.6 on the standard normal distribution curve. This can be found using a standard normal distribution table or a calculator.

Similarly, to find the area below 48 for a N(60,10) distribution, we need to calculate the probability that a value is less than 48. We can find the z-score for 48: z = (48 - 60) / 10 = -1.2

The area below 48 is equal to the area to the left of -1.2 on the standard normal distribution curve.

Answer 2

To determine the areas under the normal distribution for values above 66 and below 48 with a mean of 60 and standard deviation of 10, calculate the z-scores for both values and look up the corresponding areas using a z-table or calculator.

Step-by-step explanation:

Finding Areas Under a Normal Distribution

To find the area above 66 for a N(60, 10) distribution, we need to calculate the z-score for 66. The z-score is given by the formula:

z = (X - μ) / σ

Where X is the value in question, μ is the mean, and σ is the standard deviation. For 66, the z-score is (66 - 60) / 10 = 0.6. Using a z-table or calculator, we can find the area to the right of z = 0.6, which is the area above 66.

To find the area below 48 for a N(60, 10) distribution, we calculate the z-score for 48, which is (48 - 60) / 10 = -1.2. The area to the left of z = -1.2, which is the area below 48, can also be found using a z-table or calculator.

Note: Since a normal distribution is symmetrical, the area to the right of a positive z-score is equal to the area to the left of the same negative z-score and vice versa.