Which choice represents the fraction below as a single exponential expression?

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule t

MissTica

Answer:

A) 99.7% of people have an IQ between 64 and 136.

B) 5% of people have an IQ score less than 76 or greater than 124.

C) 16% of people have an IQ score greater than 112.

Step-by-step explanation:

The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.

A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.

B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.

C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.

8 0

3 years ago

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

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".

The population proportion have the following distribution

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

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

7 0

3 years ago

If a 10-foot piece of electrical tape has five pieces that are each 1.25 feet cut from it, what is the new length of the tape?

BartSMP [9]

5 pieces X 1.25 = 6.25

10-6.25 = 3.75 is the new length

3 0

3 years ago

If 3 out of 10 mammalian cell cultures exposed to ultraviolet (UV) radiation developed chromosomal abnormalities while 9 out of

Zina [86]

Answer:

a) Observational Study

b) Risk in observational study

RR = 9/10/3/10 = 3.0

c) Relative risk when exposed to a common NSAID is 3 out of 10 people

Step-by-step explanation:

A) This is observational study

b) The parameter determined here is the risk in observational study

RR = 9/10/3/10 = 3.0

c) Relative risk of mammalian cell to develop chromosomal abnormalities when exposed to a common NSAID is 3 out of 10 people

8 0

3 years ago

What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?

Monica [59]

Answer:

y = 4x + 16

Step-by-step explanation:

y - 1 = 4(x + 3)

Has a slope of 4

y = 4x + c

32 = 4(4) + c

32 - 16 = c

c = 16

y = 4x + 16

7 0

3 years ago

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