What is the slope and y-intercept of this equation?

The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play

Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5$

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{76 - 75}{0.5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

6 0

3 years ago

Why is there always more than one parallelogram with the same area and base

BaLLatris [955]

Answer:

If every line parallel to two lines intersects both regions in line segments of equal length, then the two regions have equal areas. In the case of your problem, every line parallel to the bases of the two parallelograms will intersect them in lines segments, each with a width of ℓ.

6 0

2 years ago

7. What is the solution to 9x = -63?<br> A. x=54<br> B. x= 7<br> C. x= -7<br> D. x = -54

Dmitry [639]

Given the equation 9x = -63, the numerical value of x is -7.

<h3>What is the solution to the given equation?</h3>

Given the equation in the question;

9x = -63

To determine the value of x, we divide both sides by the coefficient of x.

9x = -63

9x/9 = -63/9

x = -7

Given the equation 9x = -63, the numerical value of x is -7.

Learn more about equations here: brainly.com/question/14686792

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6 0

2 years ago

To add integers with the same sign

Mariana [72]

Arithmetic

-3-2=5

because

-3-2

=

-3 + -2

3 negatives + 2 negatives = 5 negatives

5 0

3 years ago

Read 2 more answers

Why does a radical function with an even index only appear on one sode of the x-axis while a radical woth an odd index appears o

Vladimir79 [104]

Consider the equation y = x^2. No matter what x happens to be, the result y will never be negative even if x is negative. Example: x = -3 leads to y = x^2 = (-3)^2 = 9 which is positive.

Since y is never negative, this means the inverse x = sqrt(y) has the right hand side never be negative. The entire curve of sqrt(x) is above the x axis except for the x intercept of course. Put another way, we cannot plug in a negative input into the square root function for this reason. This similar idea applies to any even index such as fourth roots or sixth roots.

Meanwhile, odd roots such as a cube root has its range extend from negative infinity to positive infinity. Why? Because y = x^3 can have a negative output. Going back to x = -3 we get y = x^3 = (-3)^3 = -27. So we can plug a negative value into the cube root to get some negative output. We can get any output we want, negative or positive. So the range of any radical with an odd index is effectively the set of all real numbers. Visually this produces graphs that have parts on both sides of the x axis.

3 0

3 years ago