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aleksandr82 [10.1K]
3 years ago
5

The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. I

f a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would be result in twins
Mathematics
1 answer:
nikdorinn [45]3 years ago
8 0

Answer:

mean = 160

Variance = 156.8

Standard deviation = 12.52

Step-by-step explanation:

This is solved by the binomial distribution model for approximation.

n = number of random sample in which for this question, n= 8000

p = probability of success = 2% = 0.02

Mean of the sample = Expected value which approximates the average number of cases to expect from the larger sample chosen.

Mean = np = 0.02 × 8000 = 160

Variance = np(1-p) = 160(1-0.02) = 156.8

Standard deviation = √variance = √156.8 =12.52

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The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed t
Lady bird [3.3K]

Answer:

10.08-1.64\frac{0.1}{\sqrt{6}}=10.013    

10.08+1.64\frac{0.1}{\sqrt{6}}=10.147    

So on this case the 90% confidence interval would be given by (10.013;10.147)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma =0.1 represent the population standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=10.08

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Now we have everything in order to replace into formula (1):

10.08-1.64\frac{0.1}{\sqrt{6}}=10.013    

10.08+1.64\frac{0.1}{\sqrt{6}}=10.147    

So on this case the 90% confidence interval would be given by (10.013;10.147)    

5 0
3 years ago
4 3/8+ 2 7/12 <br> Alguém sabe a resposta
Nata [24]

Answer:

6 23/24

Step-by-step explanation:

First, find the least common factor of 8 and 12, the denominators.

8 16 24

12 24

24, is now the current denominnator,

8x 3 = 24

Now you go do it to the numerator, 3 x 3 = 9

9/24 + ?

Now, 12 x 2 = 24, do it to the numerator, 7 x 2 = 14

4 9/24 + 2 14/24

Now add the front numbers to make 6, than add the numerators and keep the denominator.

6 23/24, since you can not simplify this fraction, this is the answer.

6 0
3 years ago
1. Ilove ordering cookies from Tiff's Treats (not
agasfer [191]

c = cost

h = # of half-dozens ordered

c = $8.50h + $1  is the correct answer.

4 0
3 years ago
What are 2 binomials that are factors of this trinomial? x^2-x-20
liberstina [14]

Answer:

(x-5) (x+4)

Step-by-step explanation:

x^2 -x -20

What two terms multiply to -20 and add to -1

-5*4 = -20

-5+4 = -1

(x-5) (x+4)

8 0
2 years ago
Read 2 more answers
1. What does it mean for a number to have a variable at the end of it? (i.e 1.6x)
miskamm [114]

Answer:

1. 1.6x has a variable which means an unknown number

2. 5 more than 0.10 times a number

Step-by-step explanation:

A variable is an unknown number represented by a letter. It provides a way to write a relationship in the real world without knowing all the values involved, 1.6x means 1.6 times an unknown number mathematically. A real world example would be a percent growth of 60% on an unknown price - 1.6x.

5 + 0.10x means 5 more than 0.10 times an unknown number. A real world example here would be "10% off a sale plus $5 coupon". We don't know the price of the item but we do know it is 10% off and we get $5 off. Once we know the price we input it int for x and find the total discount.

8 0
3 years ago
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