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zepelin [54]
3 years ago
12

In a random sample of 45 newborn babies, what is the probability that 40% or fewer of the sample are boys. (Use 3 decimal places

). Hint: you are asked to find P( < .40 ). To calculate this first find the z-score and then calculate the probability.
Mathematics
2 answers:
erastova [34]3 years ago
7 0

Answer:

z= \frac{p- \mu_p}{\sigma_p}

And the z score for 0.4 is

z = \frac{0.4-0.4}{\sigma_p} = 0

And then the probability desired would be:

P(p

Step-by-step explanation:

The normal approximation for this case is satisfied since the value for p is near to 0.5 and the sample size is large enough, and we have:

np = 45*0.4= 18 >10

n(1-p) = 45*0.6= 27 >10

For this case we can assume that the population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Where:

\mu_{p}= \hat p = 0.4

\sigma_p = \sqrt{\frac{p(1-p)}(n} =\sqrt{\frac{0.4(1-0.4)}(45}= 0.0703

And we want to find this probability:

P(p

And we can use the z score formula given by:

z= \frac{p- \mu_p}{\sigma_p}

And the z score for 0.4 is

z = \frac{0.4-0.4}{\sigma_p} = 0

And then the probability desired would be:

P(p

kkurt [141]3 years ago
7 0

Answer:

The probability that 40% or fewer of the sample are boys P(x ≤ 0.4) = 0.090

Step-by-step explanation:

Normally, the mean number of boys in the population should be given, but in the absence, we take 50% of the population to be boys (since, there are only two possibilities, with close probabilities).

Mean = 0.5

Standard deviation of a sample = √[p(1-p)/n]

p = 0.5

1-p = 0.5

n = sample size = 45

Standard deviation = √[(0.5×0.5)/45] = 0.0745

So, we can now standardize 0.4.

The standardized score is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0.4 - 0.5)/0.0745 = - 1.34

To determine the probability that 40% or fewer of the sample are boys P(x ≤ 0.4) = P(z ≤ -1.34)

We'll use data from the normal probability table for these probabilities

P(x ≤ 0.4) = P(z ≤ -1.34) = 0.090

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Studentka2010 [4]

Answer:

1. z^2

2. 14z

Step-by-step explanation:

  • We know that (a^m)^n = a^(mn) = (a^n) ^m

We also know that (a^m)(a^n) = a^(m+n)

  1. 36 can be written as 6^2 and here 36^(500) can be written as (6^2)^500 which also can be written as (6^500)^2 and as already it is mentioned that 6^500 as z we can write the above as <u>z^2</u>

2. 8 x 6^500 = 8z

And we can also write 6^(501) as 6^(500+1) which is equivalent to 6(6^500) which is 6z.

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7 0
3 years ago
Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, thei
poizon [28]

A. First let us start with the linear model.

The equation is in the form of y = m x + b

Calculating for the slope m:

m = (309,587 – 50,000) / (2007 – 1997)

m = 25,958.7

 

Subsituting:

y = 25,958.7 x + b

Taking x = 1997, y = 50,000. Solve for b:

50,000 = 25,958.7 (1997) + b

b = -51,789,523.9

 

The complete equation is therefore:

y = 25,958.7 x - 51,789,523.9

 

 

B. The exponential model has the following form:

y = a b^x

where a and b are constants

 

Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587

50,000 = a b^1997

309,587 = a b^2007

 

Combining in terms of a:

50,000 / b^1997 = 309,587 / b^2007

b^2007 / b^1997 = 309,587 / 50,000

b^10 = 6.19174

b = 1.2

 

Substituting:

y = a 1.2^x

 

Solving for a:

50,000 = a 1.2^1997

a = 3.75 x 10^-154

 

The complete equation is:

y = 3.75 x 10^-154 * 1.2^x

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Answer:

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Step-by-step explanation:

200 \div 5 = 40

40 = 1 \: ratio

3 \times 40 = 120

2 \times 40 = 80

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