The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 70 with a standard deviation of 9.8. Assume that the distribution is approximately normal. (a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 70 ml/kg? 0.5 (b) What is the probability that an elite athlete has a maximum oxygen uptake of 65 ml/kg or lower? (c) Consider someone with a maximum oxygen uptake of 38 ml/kg. Is it likely that this person is an elite athlete? Write "YES" or "NO."

The probability will be:

(a) 0.5

(b) 0.3050

(c) No, person isn't an elite athlete.

According to the question,

Mean,

Standard deviation,

(a)

Maximum oxygen uptake,

The probability is:

→

      (p-value of 0.5)

then,

      or 50%

(b)

→

      (p-value of 0.3050)

then,

      or, 30.50%

(c)

If it is lower than "-2", then we have to find the z-score.

→

Thus the above approach is appropriate.

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a) 0.5 = 50% probability that an elite athlete has a maximum oxygen uptake of at least 70 ml/kg

b) 0.3050 = 30.50% probability that an elite athlete has a maximum oxygen uptake of 65 ml/kg or lower

c) NO.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Z scores greater than 2 or lower than -2 means that X is considered unlikely.

In this problem, we have that:

(a) What is the probability that an elite athlete has a maximum oxygen uptake of at least 70 ml/kg?

This is 1 subtracted by the pvalue of Z when X = 70. So

has a pvalue of 0.5.

1 - 0.5 = 0.5

0.5 = 50% probability that an elite athlete has a maximum oxygen uptake of at least 70 ml/kg

b) What is the probability that an elite athlete has a maximum oxygen uptake of 65 ml/kg or lower?

This is the pvalue of Z when X = 65. So

has a pvalue of 0.3050.

0.3050 = 30.50% probability that an elite athlete has a maximum oxygen uptake of 65 ml/kg or lower

(c) Consider someone with a maximum oxygen uptake of 38 ml/kg. Is it likely that this person is an elite athlete?

We have to find the z-score. If it is lower than -2, we write no.

So the answer is NO.

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step-by-step explanation: