Answer :
To calculate the percentage of scores for each case, we can utilize the properties of a normal distribution curve with the given mean and standard deviation.
a) Between 74 and 86:
To find the percentage of scores between 74 and 86, we need to determine the area under the normal curve within these two values. First, we find the Z-scores for 74 and 86 using the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Then, we look up these Z-scores in a standard normal distribution table to find the corresponding percentages. Subtracting the percentage corresponding to 74 from the percentage corresponding to 86 gives us the percentage of scores between 74 and 86.
b) Less than 74:
To find the percentage of scores less than 74, we find the Z-score for 74 and look it up in the standard normal distribution table to obtain the percentage of scores below 74.
c) Between 68 and 92:
Follow the same steps as in part (a) to find the percentage of scores between 68 and 92.
d) Between 62 and 98:
Repeat the steps from part (a) to find the percentage of scores between 62 and 98.
e) More than 98:
To find the percentage of scores greater than 98, we find the Z-score for 98 and look up the percentage of scores below 98 in the standard normal distribution table. Subtracting this percentage from 100% gives us the percentage of scores above 98.
By following these steps and using the properties of the normal distribution, you can calculate the percentage of scores for each case accurately.
