Write an equation for the problem.Then Solve. What number is 8% of 50?

A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 173 yellow peas.

Andre45 [30]

Answer:

a

The 95% confidence interval is $0.2474 < p < 0.3188$

b

The result obtained does not contradict expectation

Step-by-step explanation:

From the question we are told that

The number of green peas is k = 438

The number of yellow peas is u = 173

Generally the sample size is mathematically represented as

$n = k + u$

=> $n = 438 + 173$

=> $n = 611$

Generally the sample proportion for yellow peas is

$\^ p = \frac{u}{n}$

=> $\^ p = \frac{173}{611 }$

=> $\^ p = 0.2831$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.96 * \sqrt{\frac{ 0.2831 (1- 0.2831)}{611} }$

=> $E = 0.0357$

Generally 95% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.2831 -0.0357$

=> $0.2474 < p < 0.3188$

From the question we are told that it was expected that 25% of the offspring peas will be yellow

Now from the 95% confidence interval obtained we see that the expected sample proportion(25% ) falls within it so it means that the result obtained does not contradict expectation

7 0

2 years ago

Distance between 1,-4and 7,-4 on a coordinate grid

MAXImum [283]

Answer:

6 units.

Step-by-step explanation:

Distance = √ [(7 - 1)^2 + (-4-(-4))^2]

= √(36 + 0)

= 6 units.

6 0

2 years ago

Please help me it’s very important, give a correct explanation

AlekseyPX

Step-by-step explanation:

triangle MAC=triangle MBD=90 Degree

Therefore, From right angled triangle

AC=BD

8 0

2 years ago

A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of

myrzilka [38]

Answer:

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

$X \sim N(60,13.5)$

Where $\mu=60$ and $\sigma=13.5$

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error of the mean would be:

$\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5$

4.1.5

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".

Solution to the problem

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

$X \sim N(60,13.5)$

Where $\mu=60$ and $\sigma=13.5$

And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error of the mean would be:

$\sigma_{\bar X} =\frac{13.5}{\sqrt{81}}= 1.5$

4.1.5

7 0

3 years ago

A study records the lengths of pregnancy (in days) of 500 women. The data is normally distributed with a mean of 266 days and a

VashaNatasha [74]

Answer:

371 women had their pregnancy between 250 days and 282 days in length.

di po ako sure sa answer ko, but it is based on what I remembered.

Step-by-step explanation:

z=532-266

16

√500

= 371.74 or 371

4 0

2 years ago