Question

(1 point) The physical fitness of a patient is often measured by the patient's maximum oxygen uptake (recorded in millilitersper kilogram, ml/kg). The mean maximum oxygen uptake for cardiac patients who regularly participate in sports or exerciseprograms was found to be 25.5, with a standard deviation of 5.7. Assume that this distribution is approximately normal.Find the following. (Note: Give answers as decimal proportions, not percentages.)

Answer 1

Since the distribution is normal and the populatin standard deviation is known, we would calculate the z score by applying the formula,

z = (x - μ)/σ

where

μ is the population mean

σ is the population standard deviation

x is the sample mean

From the information given,

μ = 25.5

σ = 5.7

a) We want to find P(x ≥ 18.1)

P(x ≥ 18.1) = 1 - P(x < 18.1)

z = (18.1 - 25.5)/5.7

z = - 1.3

P(x < 18.1) is the area to the left of z = - 1.3 on the normal distribution table. Thus,

P(x < 18.1) = 0.0968

P(x ≥ 18.1) = 1 - 0.0968

P(x ≥ 18.1) = 0.9032

The probability that a cardiac patient who regularly participates in sports has a maximum oxygen uptake of at least 18.1 ml/kg is 0.9032

b) We want to calculate P(x ≤ 10.68)

z = (10.68 - 25.5)/5.7 =

z = - 2.6

P(x ≤ 10.68) is the area to the left of z = - 2.6 on the normal distribution table. Thus,

P(x ≤ 10.68) = 0.00466

The probability that a cardiac patient who regularly participates in sports has a maximum oxygen uptake of 10.68 ml/kg or lower is 0.00466

c) Since the probability is very low, the correct option is

A. Not very likely