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kolezko [41]
3 years ago
8

A construction worker bought several bottles of juice for three dollars at the convenient store. She paid for them with a $20 bi

ll. If Jay represents the number of bottles of juice, write an expression for the change she should receive
Mathematics
1 answer:
Veronika [31]3 years ago
5 0
20-3j=change she should receive.
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19. A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years
Juliette [100K]

Answer:

a) Approximately normal.

b) The mean is 75 years and the standard deviation is 0.8485 years.

c) 0.9909 = 99.09% probability that the mean age exceeds 73 years

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}}.

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

Sample of 50 retirees

This means that n = 50

Mean age and standard deviation are 75 and 6 years

This means that \mu = 75, \sigma = 6

a. Describe the shape of the sampling distribution of the sample mean in this case

By the Central Limit Theorem, approximately normal.

b. Find the mean and standard error of the sampling distribution of the sample mean.

By the Central Limit Theorem, the mean is 75 and the standard error is s = \frac{6}{\sqrt{50}} = 0.8485

c. What is the probability that the mean age exceeds 73 years?

This is 1 subtracted by the pvalue of Z when X = 73.

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

By the Central Limit Theorem

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

Z = \frac{73 - 75}{0.8485}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

1 - 0.0091 = 0.9909

0.9909 = 99.09% probability that the mean age exceeds 73 years

5 0
2 years ago
Plz help me with the ones that are circled
Alisiya [41]
Your answer for your question is going to be.... um.... sorry I forgot
3 0
3 years ago
8 divided by (7 - 3) x ( 4 + 6)<br> Equals?
gregori [183]

8÷(7-3)x(4+6)

8÷4x10

2x10

<u>20</u>

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3 years ago
The following stem-and-leaf plot represents the scores earned by Mr. Roberts's class on their most recent science test.
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First we need to count the total number scores. This can be done from the stem and leaf plot. The total number of scores are 19. The total number of values is odd, so the median position will be:

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C is the correct answer. An equilateral triangle is a type of triangle.
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