Suppose that the distribution of resting pulse rates for 4-year-olds is bell-shaped with a mean of 108 beats per minute and a standard deviation of 8 beats per minute. Use the Empirical Rule to complete each sentence. (In each sentence enter the smaller number in the first answer blank and the larger number in the second answer blank.)(a)About 68% of 4-year-olds have a resting pulse rate between and beats per minute.(b)About 95% of 4-year-olds have a resting pulse rate between and beats per minute.(c)About 99.7% of 4-year-olds have a resting pulse rate between and beats per minute.
Question
Suppose that the distribution of resting pulse rates for 4-year-olds is bell-shaped with a mean of 108 beats per minute and a standard deviation of 8 beats per minute. Use the Empirical Rule to complete each sentence. (In each sentence enter the smaller number in the first answer blank and the larger number in the second answer blank.)(a)About 68% of 4-year-olds have a resting pulse rate between and beats per minute.(b)About 95% of 4-year-olds have a resting pulse rate between and beats per minute.(c)About 99.7% of 4-year-olds have a resting pulse rate between and beats per minute.
Solution
(a) About 68% of 4-year-olds have a resting pulse rate between 100 and 116 beats per minute. (b) About 95% of 4-year-olds have a resting pulse rate between 92 and 124 beats per minute. (c) About 99.7% of 4-year-olds have a resting pulse rate between 84 and 132 beats per minute.
Here's how we got these numbers:
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution:
- About 68% of values fall within 1 standard deviation of the mean.
- About 95% of values fall within 2 standard deviations of the mean.
- About 99.7% of values fall within 3 standard deviations of the mean.
Given that the mean is 108 beats per minute and the standard deviation is 8 beats per minute:
(a) 68% of values fall within 1 standard deviation of the mean. So, we subtract and add 8 (the standard deviation) from 108 (the mean) to get the range 100 to 116.
(b) 95% of values fall within 2 standard deviations of the mean. So, we subtract and add 2*8=16 from 108 to get the range 92 to 124.
(c) 99.7% of values fall within 3 standard deviations of the mean. So, we subtract and add 3*8=24 from 108 to get the range 84 to 132.
Similar Questions
Suppose that head circumferences of adult men have a bell-shaped distribution with mean = 58 cm and standard deviation = 3 cm. (Use the Empirical Rule.)(a)What is the head circumference (in cm) such that only 2.5% of adult men have a smaller head circumference? cm(b)What is the head circumference (in cm) such that only 2.5% of adult men have a larger head circumference? cm(c)What is the head circumference (in cm) such that only 16% of adult men have a larger head circumference? cm
Use the Empirical Rule to answer the question.A highway study of 6,000 vehicles that passed by a checkpoint found that their speeds were normally distributed, with a mean of 66 mph and a standard deviation of 7 mph.(a)How many of the vehicles had a speed of more than 73 mph? vehicles(b)How many of the vehicles had a speed of less than 45 mph?
According to the empirical rule for normally distributed data, what percent of data would fall within two standard deviations of the mean?A13.5 %
Use the Empirical Rule to answer each question.During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 28 ounces and a standard deviation of 7 ounces.(a) What percent of the parcels weighed between 14 ounces and 35 ounces? (Round your answer to one decimal place.) %(b) What percent of the parcels weighed more than 49 ounces? (Round your answer to two decimal places.) %
Use the Empirical Rule to establish an interval that includes about 95% of the observations.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.