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3 years ago

Kasey asked 6 of her friends how many episodes of their favorite show they

Mathematics

1 answer:

ivanzaharov [21]3 years ago

3 0

Answer:

Step-by-step explanation:

6 friends

Mean - 10

Median - 9.5

Range - 14

3 friends watched 12, 13, and 18 movies.

Let's find the sum, this will help us find the total number of movies the other 3 friends watched.

12 + 13 + 18 = 43

The mean is all their movies added toether, divided by the number of friends.

m = number of movies the other friends watched.

(43 + m) / 6 = 10 Multiply each side by 6

43 + m = 10 * 6

43 + m = 60 Subtract 43 from each side

m = 60 - 43

m = 17

So we know the total movies the other friends watched is 3.

A. 4+6+7 = 17

B. 4+4+7 = 15

C. 5+8+9 = 22

D. 2+3+5 = 10

We know the answer is A.

We can check it by looking at the Median, the median is the middle number, if there are an even number of samples, you add the 2 middle numbers together and divide by 2.

4, 6, 7, 12, 13, 18

So 7+12 = 19

19/2 = 9.5

So we know for sure A is correct!

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Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 $s = \frac{\sigma}{\sqrt{n}}$ .