Mathematics, 19.06.2020 20:57 graceshort7orepzg

The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than 19 minutes,
(b) between 24 and 33 minutes, and
(c) more than 40 minutes.

Which event is unusual?

The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a me

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Answer from: jakhunter354

(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is 0.2388.

(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is 0.3997.

Step-by-step explanation:

We are given that the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.

Let X = amounts of time per workout an athlete uses a stairclimber

So, X ~ Normal( $\mu=24,\sigma^{2} =7^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 24 minutes

$\sigma$ = standard deviation = 7 minutes

(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is given by P(X < 19 minutes)

P(X < 19 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{19-24}{7}$ ) = P(Z < -0.71) = 1 - P(Z $\leq$ 0.71)

= 1 - 0.7612 = 0.2388

The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.

(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is given by = P(24 min < X < 33 min)

P(24 min < X < 33 min) = P(X < 33 min) - P(X $\leq$ 24 min)

P(X < 33 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{33-24}{7}$ ) = P(Z < 1.28) = 0.8997

P(X $\leq$ 24 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{24-24}{7}$ ) = P(Z $\leq$ 0) = 0.50

The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.

Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997

(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is given by P(X > 40 minutes)

P(X > 40 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{40-24}{7}$ ) = P(Z > 2.28) = 1 - P(Z $\leq$ 2.28)

= 1 - 0.9887 = 0.0113

The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.

The event of probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.

Answer from: Quest

isi

step-by-step explanation:

use that smart brain

Answer from: Quest

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?

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