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mylen [45]
1 year ago
15

What is the sum of 2,480 - 170

Mathematics
2 answers:
Natalija [7]1 year ago
6 0

Answer:

2,310

Step-by-step explanation:

Vesna [10]1 year ago
6 0

2310

brainiest pls

thankyou

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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
The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 50 yd , find its length and width.
leva [86]
Length = w+3
P = 2L +2W
50 = 2(w+3) + 2w
50 = 2w +6 +2w
50 = 4w +6
50-6 =4w-6
44 = 4w
44/4 = 4w/4
w = 11
l = 11+3
l = 14

50 = 2L+2W
50 = 2(14) + 2(11)
50 = 28 +22
50=50

7 0
3 years ago
Factorise each of the following.
kupik [55]

Step-by-step explanation:

a) 2(32-4j+8k-jk)

b)a(3a-ab+3c -bc)

c)m(2m - mn + 2n - n^2)

5 0
3 years ago
12x - 16 = 68<br> Solve for x
cricket20 [7]

Answer:

x = 7

Step-by-step explanation:

12x - 16 = 68

Add 16 to each side

12x - 16+16 = 68+16

12x =84

Divide by 12

12x/12 = 84/12

x = 7

6 0
3 years ago
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an hourglass is turned over with the top part filled with sand. after 3 minutes, there are 855 ml of sand in the top half. after
Hitman42 [59]

An hourglass is turned over with the top part filled with sand. after 3 minutes, there are 855 ml of sand in the top half. after 10 minutes, there are 750 ml of sand in the top half. This can be represents a two points ( 3, 855) and (10, 750) . using this to solve the slope m = (750-855)/(10-3) = -15. And using one point the equation is y = -15x + 900.

5 0
2 years ago
Read 2 more answers
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