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3 years ago

Which of these variables is least likely to have a normal distribution?

Mathematics

2 answers:

Ainat [17]3 years ago

8 0

Answer:

Annual income for all 150 employees at a local high school

Step-by-step explanation:

The normal distribution is also called the Gaussian distribution. It is the most common type of distribution for statistical analysis. The normal distribution is based on a probability distribution. The data near the mean are more frequent than the data away from the mean. It is based on two parameters: the mean and the standard deviation.

As per options, option A which states ‘annual income for all 150 employees at a local high school’ the data is within the standard deviation.

Viefleur [7K]3 years ago

4 0

It would be a, because some of the students could have really high income and some low, it’s very unpredictable, but all others will probably all be very close

Hope this helps!

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High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high

KengaRu [80]

Answer:

1. It is not appropriate to use the normal curve, since np = 7.4 < 10.

2. The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

Step-by-step explanation:

Binomial approximation to the normal:

The binomial approximation to the normal can be used if:

np >= 10 and n(1-p) >= 10

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be 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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The proportion of U.S. adults with high blood pressure is 0.2. A sample of 37 U.S. adults is chosen.

This means, respectively, that $p = 0.2, n = 37$

Is it appropriate to use the normal approximation to find the probability that more than 48% of the people in the sample have high blood pressure?

np = 37*0.2 = 7.4 < 10

So not appropriate.

It is not appropriate to use the normal curve, since np = 7.4 < 10.

Part 2:

Now n = 82, 82*0.2 = 16.4 > 10, so ok

Mean and standard deviation:

By the Central Limit Theorem,

Mean $\mu = p = 0.2$

Standard deviation $s = \sqrt{\frac{0.2*0.8}{82}} = 0.0442$

Find the probability that more than 32% of the people in this sample have high blood pressure.

This probability is 1 subtracted by the pvalue of Z when X = 0.32. So

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

By the Central Limit Theorem

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

$Z = \frac{0.32 - 0.2}{0.0442]$

$Z = 2.72$

$Z = 2.72$ has a pvalue of 0.9967.

1 - 0.9967 = 0.0033

The probability that more than 32% of the people in this sample have high blood pressure is 0.0033 = 0.33%.

5 0

3 years ago

3 1/3 ÷ 2 1/2=....................

Helga [31]

So first let’s make them improper. that will then make the equation 10/3 divided by 5/2 then you want to flip one so you can divide... that would be 3/10 divided by 5/2 and then you multiply across and get 10/6

6 0

3 years ago

22.

eduard

Answer:5:1

Step-by-step explanation:

3/4 of 24=18

1/4 of 24=6

18+12=30

Wins=30

Losses=6

30:6=5:1

8 0

3 years ago

A pair of beats solo3 was marked down by ¼ of the original price. If tge sales orice is $289.00 what is the original price?

Anika [276]

The original price is $385.33

6 0

3 years ago

Which expression is equivalent to sec2x − 1?

evablogger [386]

$sec(2x)-1 \\ \\ \frac{1}{cos(2x)} -1 \\ \\ \frac{1}{1-2 sin^{2}(x) } -1\\ \\ \frac{1}{1-2 sin^{2}(x) } - \frac{1-2 sin^{2}(x) }{1-2 sin^{2}(x) } \\ \\ \frac{2 sin^{2}(x) }{1-2 sin^{2}(x) }$

3 0

3 years ago