Mathematics, 21.04.2020 18:32 neariah24

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association

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Answer from: ijohnh14

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

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

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

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10

P(Z > $\frac{x-460}{40}$ ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

$\frac{x-460}{40} =1.2816$

${x-460}{} =1.2816\times 40$

= 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Answer from: Quest

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.

the distance y is the side opposite to angle x in the right triangle. use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

Hurry i need your (50 points) the moon forms a right triangle with the earth and the sun during one

Answer from: Quest

+1,000)=g7e=mc2-g=7 because if you know algebra you should know g=7 to get your answer

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