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Ulleksa [173]
3 years ago
14

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11. Use the TI-84 Plus calculator. (a) I

s it appropriate to use the normal distribution to find probabilities for x? (b) Find the probability that x will be between 54 and 55. Round the answer to at least four decimal places. (c) Find the 47th percentile of x. Round the answer to at least two decimal places. (a) Is it appropriate to use the normal distribution to find probabilities for x? Yes No (b) Theprobabilitythatxwillbebetween54and55is. (c) The47thpercentileofxis.
Mathematics
1 answer:
sukhopar [10]3 years ago
8 0

Answer:

a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

b) There is a 15.97% probability that x will be between 54 and 55.

c) The 47th percentile of x is X = 52.877.

Step-by-step explanation:

Problems of normally distributed samples 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}

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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.

This means that \mu = 53.

We have to find the standard deviation of the sample, that is:

\sigma = \frac{11}{\sqrt{45}} = 1.64

(a) Is it appropriate to use the normal distribution to find probabilities for x?

We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

(b) Find the probability that x will be between 54 and 55.

This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.

X = 55

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

Z = \frac{55 - 53}{1.64}

Z = 1.22

Z = 1.22 has a pvalue of 0.88877.

X = 54

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

Z = \frac{54 - 53}{1.64}

Z = 0.61

Z = 0.61 has a pvalue of 0.72907.

So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.

(c) Find the 47th percentile of x. Round the answer to at least two decimal places.

This is the value of X when Z has a pvalue of 0.47;

This is between Z = -0.07 and Z = -0.08. So we use Z = -0.075.

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

-0.075 = \frac{X - 53}{1.64}

X = 52.877

The 47th percentile of x is X = 52.877.

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Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways
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gavmur [86]

Answer:

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Nemo:4x+2y=10

Step-by-step explanation:

Let x and y represent tacos and double Deckers respectively.

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Writing an equation the statement, we obtain

3x+3y=11.25

Also,for four tacos and two double Deckers, Nemo pays $10

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\boxed{d-4

<h2>Explanation:</h2>

Hello! Recall you need to write complete questions in order to find exact answers. So in this problem I'll assume the question is:

<em>A number d minus 4 is less than -1</em>

<em />

So it is easy to know that we need to write an inequality here because of the words "less than", which implies that we must use the symbol <. So let's solve this step by step.

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<h2>Learn more:</h2>

Inequalities: brainly.com/question/9611462

#LearnWithBrainly

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