Question

For a certain group of individuals, the average heart rate is 80 beats per minute, with a standard deviation of 3 beats. If a subject is selected at random, find the following, show your work:

a. between 75 and 85 beats per minute.

b. between 81 and 86 beats per minute.

c. between 76 and 79 beats per minute.

Answer 1

Solution :

Given that,

mean = = 80

standard deviation = = 3

a ) P (75 < x < 85 )

P ( 75 - 80 / 3) < ( x -  / ) < (85 - 80 / 3)

P ( - 5 / 3 < z < 5 / 3 )

P (-1.67 < z < 1.67)

P ( z < 1.67 ) - P ( z < -1.67)

Using z table

= 0.9525 - 0.0475

= 0.9050

Probability = 0.9050

b ) P (81 < x < 86 )

P ( 81 - 80 / 3) < ( x -  / ) < (86 - 80 / 3)

P ( 1 / 3 < z < 6 / 3 )

P (0.33 < z < 2 )

P ( z < 2 ) - P ( z < 0.33)

Using z table

= 0.9772- 0.6293

= 0.3479

Probability = 0.3479

c ) P (76< x < 79 )

P ( 76 - 80 / 3) < ( x -  / ) < (79- 80 / 3)

P ( - 4 / 3 < z < - 1 / 3 )

P (-1.33 < z < - 0.33)

P ( z < - 0.33 ) - P ( z < -1.33)

Using z table

= 0.3707 -0.0918

= 0.2789

Probability = 0.2789