What additional piece of information must be known in order to calculate the volume of the cylinder below?

Decide whether the two expressions are equivalent for each problem below.

Vesnalui [34]

Answer:

Step-by-step explanation:

6 0

2 years ago

Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are

Sergeu [11.5K]

Answer:

D. 0.9938.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 115 and a standard deviation of 8.

This means that $\mu = 115, \sigma = 8$

100 people are randomly selected

This means that $n = 100, s = \frac{8}{\sqrt{100}} = 0.8$

Find the probability that their mean blood pressure will be less than 117.

This is the p-value of Z when X = 117, so:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{117 - 115}{0.8}$

$Z = 2.5$

$Z = 2.5$ has a p-value of 0.9938, and thus, the correct answer is given by option D.

8 0

3 years ago

What number is to 100 as 4 is to 78

vitfil [10]

Hello,

4 is to 78 as x is to 100, we write it as a ratio:

$\frac{4}{78}= \frac{x}{100} \\ \\ x= \frac{100*4}{78} \\ \\ \boxed{x= \frac{200}{39}=5.13}$

5 0

3 years ago

About 543 out of every 1,000 people in United States owned a cell phone in 2003.In japan,the are was 68 for every 100 people.How

Softa [21]

Answer:

The greater percent of cell phone ownership in Japan than the U.S was <u>13.7%</u>.

Step-by-step explanation:

Given:

About 543 out of every 1,000 people in United States owned a cell phone in 2003.

In japan,the are was 68 for every 100 people.

Now, to find the greater percent of cell phone ownership in Japan than the U.S.

So, to get the percent of people owned cell phone in United States:

$\frac{543}{1000}\times 100$

$=0.543\times 100$

$=54.3\%.$

Now, to get the percent of people owned cell phone in Japan:

$\frac{68}{100} \times 100\\\\=0.68\times 100\\\\=68\%.$

So, to get the percent greater of cell phone ownership in Japan than the U.S we subtract the percent of people owned cell phone in United States from the percent of people owned cell phone in Japan:

$68\%-54.3\%\\\\=13.7\%.$

Therefore, the greater percent of cell phone ownership in Japan than the U.S was 13.7%.

5 0

3 years ago

Suppose that you are given a bag containing n unbiased coins. You are told that n-1 of these coins are normal, with heads on one

gladu [14]

Answer:

The (conditional) probability that the coin you chose is the fake coin is 2/(1 + n)

Step-by-step explanation:

Given

Total unbiased coin = n

Normal coins =n - 1

Fake = 1

The (conditional) probability that the coin you chose is the fake coin is represented by

P(Fake | Head)

And it's calculated as follows;

P(Fake | Head) = P(Fake, Head) ÷ P(Head) ----- (1)

Where P(Fake, Head) = P(Fake) * P(Head | Fake)

P(Fake) = 1/n --- because only one is fake

P(Head | Fake) = n/n because all coins (including the fake) have head

So, P(Fake, Head) = P(Fake) * P(Head | Fake) becomes

P(Fake, Head) = 1/n * n/n

P(Fake, Head) = 1/n

P(Head) is calculated by

P(Fake) * P(Head | Fake) + P(Normal) * P(Head | Normal)

P(Fake) * P(Head | Fake) = P(Fake, Head) = 1/n (as calculated above)

P(Normal) * P(Head | Normal) = ½ * (n - 1)/n ----- considering that the coin also has a tail with equal probability as that of the head.

Going back to (1)

P(Fake | Head) = P(Fake, Head) ÷ P(Head) becomes

P(Fake | Head) = (1/n) ÷ ((1/n) + (½(n-1)/n))

= (1/n) ÷ ((1/n) + (½(n-1)/n))

= (1/n) ÷ (1/n + (n - 1)/2n)

= (1/n) ÷ (2 + n - 1)/(2n)

= (1/n) ÷ (1 + n)/(2n)

= (1/n) * (2n)/(1 + n)

= 2/(1 + n)

Hence, the (conditional) probability that the coin you chose is the fake coin is 2/(1 + n)

5 0

3 years ago