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DanielleElmas [232]
2 years ago
7

Iq scores are normally distributed with a mean of 100 and a standard deviation of 15.

Mathematics
1 answer:
bearhunter [10]2 years ago
6 0

Mean is \mu=100 and a standard deviation is \sigma =15, then the variable X\sim N(100,15^2).

Use substitution

Z=\dfrac{X-\mu}{\sigma},\\  \\ Z=\dfrac{X-100}{15}.

This substitution gives you that Z\sim N(0,1).

a. For X=130, Z=\dfrac{130-100}{15}=2 and Pr(X>130)=Pr(Z>2) =0.9772 (the decimal value is taken from the Standard Normal Distribution Table).

b. For X=90, Z=\dfrac{90-100}{15}=-\dfrac{2}{3} and for X=110, Z=\dfrac{110-100}{15}=\dfrac{2}{3}. Then Pr(90 (the decimal value is taken from the Standard Normal Distribution Table).

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A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 335335 babies were​ born
strojnjashka [21]

Answer:

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

Step-by-step explanation:

Confidence Interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 335, \pi = \frac{268}{335} = 0.8

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{335}} = 0.7437

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{335}} = 0.8563

For the percentage:

Multiplying the proportions by 100.

The 99​% confidence interval estimate of the percentage of girls born is (74.37%, 85.63%).

Usually, 50% of the babies are girls. This confidence interval gives values considerably higher than that, so the method to increase the probability of conceiving a girl appears to be very effective.

7 0
3 years ago
If ?2000 is placed into a bank account that pays 3% compound interest per year,how much will be in the account after 2 years?
Ipatiy [6.2K]

Answer:

There would be $2,120

Step-by-step explanation:

First figure out what 3% of 2000 is which is 60. Multiply the 60 by 2 to get 120 then add 120 to 2000

3 0
3 years ago
Read 2 more answers
Solve for x please refer to image
QveST [7]

Answer:

x = 40

Step-by-step explanation:

Sum of interior angle of an n-polygon = (n - 2)*180

The polygon given is pentagon with 5 sides.

Sum of the polygon = (5 - 2)*180 = 540°

Therefore, sum of all its interior angles would be:

5x + 150 + (3x - 30) + 70 + (2x - 50) = 540°

Solve for x

5x + 150 + 3x - 30 + 70 + 2x - 50 = 540

Collect like terms

5x + 3x + 2x + 150 - 30 + 70 - 59 = 540

10x + 140 = 540

10x = 540 - 140 (Subtraction property of equality)

10x = 400

x = 400/10 (division property of equality)

x = 40

6 0
2 years ago
It costs $6 to take 1 dog to the beach. It costs $1 more for each additional dog. Which is the equation, when x=1?
Leni [432]
6+1x= 7 ::::::::::::::::::::::::::::::::::
6 0
3 years ago
What is 7/7-1/5= ?<br> Is it.....<br><br> 8/12<br><br> 18/35<br><br> 28/35<br><br> 6/35
Elza [17]
1-(1/5)= 4/5 or 28/35 if you multiply top and bottom by 5
8 0
3 years ago
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