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3 years ago

2. Find the mode of the following data:

Mathematics

2 answers:

LUCKY_DIMON [66]3 years ago

8 0

Answer:

1) 3,1,5,6,3,4,5,3

2) Marks obtained 15 17 20

22 25

Number of students 6 17

12 18 13

stealth61 [152]3 years ago

6 0

Answer:

1)3 is the mode because it has the highest frequency

2)17

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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% 40 % of this population pref

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Answer: 60% would like another color

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3 years ago

A ski resort gets an average of 2,000 customers per weekday with a standard deviation of 800 customers. Assume the underlying di

ladessa [460]

Answer:

0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays

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:

$\mu = 2000, \sigma = 800, n = 4, s = \frac{800}{\sqrt{4}} = 400$

Trobability a ski resort averages more than 3,000 customers per weekday over the course of four weekdays.

This is 1 subtracted by the pvalue of Z when X = 3000. So

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

By the Central Limit Theorem

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

$Z = \frac{3000 - 2000}{400}$

$Z = 2.5$

$Z = 2.5$ has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that a ski resort averages more than 3,000 customers per weekday over the course of four weekdays

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3 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

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3 years ago

E : f = 2 : 3 and f : g = 7 : 8 Work out e : g Give your answer in its simplest form.

stiv31 [10]

Answer:

e : g = 7:9

Step-by-step explanation:

Given:

e : f = 2 : 3

f : g = 7 : 8

Find:

e : g

Computation:

(e/f) x (f/g) = (2/3)(7/8)

e/g = 7/9

e : g = 7:9

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3 years ago