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Answer :
Approximately 68% of people have an IQ between 100 and 130, while approximately 16% have an IQ less than 85. Additionally, 95% of people have an IQ between 70 and 130. Of the state's 9,000 full-time community college teachers, approximately 5,580 are 50 years old or younger, and the proportion of teachers aged 30 or younger is 5%.
a. According to the empirical rule for a normal distribution, approximately 68% of people have an IQ within one standard deviation of the mean. Therefore, the percentage of people with an IQ between 100 and 130 is approximately 68%.
b. Similarly, approximately 16% of people have an IQ less than one standard deviation below the mean. Therefore, the percentage of people with an IQ less than 85 is approximately 16%.
c. The 95% confidence interval in the empirical rule corresponds to approximately two standard deviations above and below the mean. Therefore, the IQ range for 95% of people is between 70 and 130.
a. If a 50-year-old teacher is in the 62nd percentile, it means that 62% of teachers are younger than 50. To find the number of teachers who are 50 years old or younger, we calculate:
Number of teachers aged 50 or younger = 62% of 9,000
Number of teachers aged 50 or younger = 0.62 × 9,000 = 5,580 teachers.
b. If 450 of the 9,000 teachers are 30 years old or younger, we can calculate the proportion (P) of teachers who are 30 years old or younger:
P = Number of teachers aged 30 or younger / Total number of teachers
P = 450 / 9,000
P = 0.05
Therefore, the proportion of teachers who are 30 years old or younger is 0.05 or 5%.
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