Question

Assume the resting heart rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 20. Use the​ 68-95-99.7 rule to find the following quantities.

a. The relative frequency of rates less than 110 using the​ 68-95-99.7 rule is ​(Round to three decimal places as​ needed.)

b. The relative frequency of rates greater than 90 using the​ 68-95-99.7 rule is nothing. ​(Round to three decimal places as​ needed.)

c. The relative frequency of rates between 30 and 70 using the​ 68-95-99.7 rule is nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Given that

mean = 70

standard deviation = 20

(A) we have to find probability that the rates less than 110

we can write 110 as 70+2*20 or mean+ 2*sd

so, 110 is 2 standard deviation above the mean

using the​ 68-95-99.7 rule, 97.7% of data is below 2 standard deviation above the mean

so, answer is 0.977

(B)

we have to find probability that the rates more than 90

we can write 90 as 70+1*20 or mean+ 1*sd

so, 90 is 1 standard deviation above the mean

using the​ 68-95-99.7 rule, 15.9% of data is above 1 standard deviation of the mean

so, answer is 0.159

(C) We can write 30 as 70-2*20 or mean - 2*sd

so, 30 is 2 standard deviation below the mean and 70 is the mean

using the​ 68-95-99.7 rule, 47.7% of data is between 2 standard deviation below the mean and the mean itself

so, answer is 0.477