Please help!! Need this done quickly. I honestly don’t get it

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

AlekseyPX

Answer:

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;

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

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

$x$ = 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.

8 0

3 years ago

What is the solution to 4(x-1)-2(3x+5)=-3x-1

Margarita [4]

To solve this problem, we need to get the variable x alone on one side of the equation. To begin, we are going to use the distributive property twice on the left side of the equation to expand the multiplication and get rid of the parentheses.

4(x-1) - 2(3x + 5) = -3x -1

4x - 4 -6x - 10 = -3x - 1

Next, we should combine like terms on the left side of the equation. This means we should add/subtract the variable terms and the constant terms in order to simplify this equation further.

-2x - 14 = -3x - 1

Then, we have to add 3x to both sides of the equation to get the variable terms all on the left side of the equation.

x - 14 = -1

After that, we should add 14 to both sides of the equation to get the variable x alone one the left side of the equation.

x = 13

Therefore, the answer is 13.

Hope this helps!

4 0

3 years ago

Read 2 more answers

Which name does not apply to the figure? A. quadrilateral B. square C. parallelogram D. rhombus

aivan3 [116]