A distribution of values is normal with a mean of 114.5 and a standard deviation of 23.
Find P47, which is the score separating the bottom 47% from the top 53%.
P47 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answers

Answer 1

Answer:

The score separating the bottom 47% from the top 53% is 112.8

Step-by-step explanation:

Let X denote the random variable whose values are normal with a mean of 114.5 and a standard deviation of 23.

Compute the 47th percentile as follows:

[tex]P(X<x)=0.47\\\\P(\frac{X-\mu}{\sigma}<\frac{x-114.5}{23})=0.47\\\\P(Z<z)=0.47[/tex]

The corresponding z-value is,

z = -0.075

*Use the z-table.

Compute the value of x as follows:

[tex]\frac{x-114.5}{23}=-0.075\\\\x=114.5-(0.075\times 23)\\\\x=112.775\\\\x\approx 112.8[/tex]

Thus, the score separating the bottom 47% from the top 53% is 112.8


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CORRECT (SELECTED)

Marcelina spends less than the intended amount of money and buys the correct amount of corn.

Point DDD is below line aaa, so it represents a scenario where she spends less than \$12$12dollar sign, 12. Also, point DDD is on line bbb, so it represents a scenario where she does buy 50\,\text{kg}50kg50, start text, k, g, end text of corn.

pasted from Khan Aacdemy

Marcelina spends less than the intended amount of money and buys the correct amount of corn.

What is an equation?

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The system of equations for the given scenario is:-

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Point D is below line a, it represents a scenario where she spends less than $12.  Also, point D is on line b, it represents a scenario where she does buy 50kg of corn.

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Percentage increase  = 7.89%

Hence, the percentage increase is 7.89%.

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Step-by-step explanation:

neosbs elenelend sidn

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