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3 years ago

14

Find the indicated probability by using the complementation rule. A percentage distribution is given below for the size of famil

ies in one U.S. city. Size Percentage 2 39.9 3 24.4 4 20.1 5 10.8 6 3.3 7 1.5 A family is selected at random. Find the probability that the size of the family is 4 or more. Round results to three decimal places.
a. 0.156
b. 0.844
c. 0.357
d. 0.201

1 answer:

arlik [135]3 years ago

7 0

Answer:

The correct option is c.

Step-by-step explanation:

The percentage probability distribution is:

Size (X) Percentage

2 39.9

3 24.4

4 20.1

5 10.8

6 3.3

7 1.5

Total 100.0

Compute the probability that the size of the family is 4 or more as follows:

P (X ≥ 4) = P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7)

= 0.201 + 0.108 + 0.033 + 0.015

= 0.357

Thus, the probability that the size of the family is 4 or more is 0.357.

The correct option is c.

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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and

egoroff_w [7]

Answer:

a) $P(140$

$P(0.036$

$P(0.036$

b) $P(140< \bar X$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(139,28.1)$

Where $\mu=139$ and $\sigma=28.1$

We are interested on this probability

$P(140$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(140$

And we can find this probability like this:

$P(0.036$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(0.036$

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)$

And the new z score would be:

$Z=\frac{\bar X -\mu}{\sigma_{\bar x}}$

$P(140< \bar X$

$P(140< \bar X$

5 0

3 years ago

Suppose that a random sample of 10 adults has a mean score of 62 on a standardized personality test, with a standard deviation o

aniked [119]

Answer:

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*\frac{4}{\sqrt{10}} = 2.08$

The lower end of the interval is the sample mean subtracted by M. So it is 62 - 2.08 = 59.92

The upper end of the interval is the sample mean added to M. So it is 62 + 2.08 = 64.08.

The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.

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2 years ago

To complete a task in 16 days a company needs

Kitty [74]

Answer: depends on the task.

Step-by-step explanation: If it is one where it is for an important person, make anyone available do it. If it's very complicated, get your smartest person do it. Not very complicated, ask for anyone who is up for the job.

7 0

2 years ago

What is the slope that connects the two points ( -1,-2) and (4,4)<br> 8th grade math.

Aleks04 [339]

Answer:

6/5

Step-by-step explanation:

rise/run

I hope this is right! :D

6 0

2 years ago

Read 2 more answers

Item 12 You win an online auction for a toy. Your winning bid of $52 is 65% of your maximum bid. How much more were you willing

nataly862011 [7]

Answer:

$28

Step-by-step explanation:

Given that:

Value of Winning bid = $52

Winning bid 65% of the maximum bid.

To find:

How much more is the maximum bid from the winning bid ?

Solution:

We are given that the winning bid is 65% of the maximum bid.

Using this percentage value, we need to first find the value of maximum bid and then we need to subtract the value of winning bid from the maximum bid to find the answer.

Let the value of maximum bid = $ $x$

As per question statement:

$65%\ of\ x = 52\\\Rightarrow \dfrac{65}{100} \times x =52\\\Rightarrow 5x = 400\\\Rightarrow x = \dfrac{400}{5}\\\Rightarrow x =\$80$

Therefore, maximum bid = $80

Our answer is:

$80 - $52 = <em>$28</em>

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3 years ago