High School

The average amount of time adults with healthy lungs can hold their breath is 50 seconds, with a standard deviation of 6 seconds. This variable is known to be normally distributed. Assuming that holding one's breath for a duration longer than the average is not a problem, with a margin of error of 4% in our decision, what is the lowest duration of breath-holding for a patient to NOT be considered ill?

A. 51.7
B. 39.5
C. 54.2
D. 45.8
E. 60.5
F. 41.5

Answer :

Given:

- Average duration m of breath-holding for adults = 50 seconds

- Standard deviation s of breath-holding durations = 6 seconds

- Margin of error in decision = 4%

We want to find the lowest duration x of breath-holding for a patient to NOT be considered ill.

We need to find the z-score corresponding to the 4% margin of error. This z-score can be found using a standard normal distribution table or calculator. A z-score of -1.750 corresponds to the 4th percentile.

Using the formula for the z-score:

z = x-m/s

We rearrange the formula to solve for x:

x=z*s+m

Substitute the values:

x= -1.75*6+50

Calculate:

x= -10.5+50=39.5

Therefore, the lowest duration of breath-holding for a patient to NOT be considered ill is approximately 39.5 seconds.

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