5-2i-2(3+i) can you help me with this answer

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.

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3 years ago

Which statement best describes the solution to this system of equations?

kondaur [170]

Answer:

x=-3

y=26

Step-by-step explanation:

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3 years ago

What would be the correlation between the ages of husbands and wives if men always married woman who were(a) 3 years younger tha

Allushta [10]

Answer:

the correct answer is a

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3 years ago

What is the value of A

Keith_Richards [23]

I think the answer is a = 4.5

81 ÷ 6 ÷ 3 = 4.5

I hope this helps, have a wonderful day!

3 0

3 years ago

Read 2 more answers

A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decre

Dmitry [639]

Using the t-distribution, it is found that since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

At the null hypothesis, it is tested if the consumption is not different, that is, if the subtraction of the means is 0, hence:

$H_0: \mu_1 - \mu_2 = 0$

At the alternative hypothesis, it is tested if the consumption is different, that is, if the subtraction of the means is not 0, hence:

$H_1: \mu_1 - \mu_2 \neq 0$

Two groups of 22 patients, hence, the standard errors are:

$s_1 = \frac{45.1}{\sqrt{22}} = 9.6154$

$s_2 = \frac{26.4}{\sqrt{22}} = 5.6285$

The distribution of the differences is has:

$\overline{x} = \mu_1 - \mu_2 = 52.1 - 27.1 = 25$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{9.6154^2 + 5.6285^2} = 11.14$

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{25 - 0}{11.14}$

$t = 2.2438$

The p-value of the test is found using a two-tailed test, as we are testing if the mean is different of a value, with t = 2.2438 and 22 + 22 - 2 = 42 df.

Using a t-distribution calculator, this p-value is of 0.0302.

Since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.

A similar problem is given at brainly.com/question/25600813

4 0

3 years ago