Question

A career counselor gives all of her new clients a measure of career maturity that scores people on a 100 point scale from 1-100. after collecting data on over 100 clients, she notices that the scores are normally distributed. The mean score is 65, indicating a level of moderate career maturity. The standard deviation of scores is 10. Based on this information, she would expect that 68% of scores would be between:

A) 55 and 75
B) 45 and 85
C) 60 and 70
D) 50 and 80

Answer 1

The range between 55 and 75 contains 68% of the scores in a normal distribution with a mean of 65 and a standard deviation of 10. Therefore, the correct answer is option A: 55 and 75.

Step-by-step explanation:

The student has asked which range of scores would contain 68% of the population, given that the scores are normally distributed with a mean of 65 and a standard deviation of 10. In a normal distribution, 68% of the data falls within one standard deviation of the mean. Therefore, to find the range, we need to add and subtract one standard deviation from the mean.

The calculation goes as follows: Mean ± Standard Deviation = 65 ± 10, which gives us:

• Lower bound = 65 - 10 = 55
• Upper bound = 65 + 10 = 75

Thus, the range that contains 68% of the client scores is from 55 to 75. This corresponds to option A: 55 and 75.