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4 years ago

Urgent help please

Mathematics

1 answer:

andrew-mc [135]4 years ago

6 0

Mean is the arithmatic average of a given data set. So,

$Mean= \frac{Sum of the data}{Number of the data}$

There are seven data in the data set.

According to the given problem,

$\frac{18+p+13+q+15+r+7 }{7} =11$

$\frac{53+p+q+r }{7} =11$ Combine the like terms of the numerator.

$\frac{53+p+q+r }{7}*7 =11 *7$ Multiplying 7 to each sides of equation.

53 + p + q + r = 77

53 + p + q + r - 53 = 77 - 53 Subtract 53 from each sides.

p + q + r = 24

Next step is to divide each sides by 3 so that we can write this in form of mean of p, q and r. Therefore,

$\frac{p + q + r}{3} =\frac{24}{3}$

So, mean of p, q and r = 8.

I hope this helps you!.

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A z-score represents the distance from $\\ \mu$ in standard deviations units. When the value for z is negative, it "tells us" that the raw score is below $\\ \mu$ . Conversely, when the z-score is positive, the standardized raw score, x, is above the mean, $\\ \mu$ .

Solving the question

We already know that $\\ z = -0.84$ or that the standardized value for a raw score, x, is below $\\ \mu$ in 0.84 standard deviations.

The values for probabilities of the standard normal distribution are tabulated in the standard normal table, which is available in Statistics books or on the Internet and is generally in cumulative probabilities from negative infinity, - $\\ \infty$ , to the z-score of interest.

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Find the cumulative standard normal table.
In the first column of the table, use -0.8 as an entry.
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The intersection of these two numbers "gives us" the cumulative probability for z or $\\ P(z$ .

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This represent the area under the standard normal distribution, $\\ N(0,1)$ , at the left of z = -0.84.

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The below graph shows the shaded area (in blue) for $\\ P(z$ for $\\ N(0,1)$ .

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