Aanand earns Rs 80 in 7 hours and pramode earns Rs 90 in 12 hours. find their ratio

What is the area of a square, if a side measures 12 cm?

Westkost [7]

Area of a square is length times by itself (length x width) so 12 cm x 12 cm
144cm squared
hope i helped :)

3 0

3 years ago

The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mea

zheka24 [161]

Answer:

$301 - $397

Step-by-step explanation:

Using the Empirical rule

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

2)95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From the above question,

Mean = 349 , standard deviation = 24.

Confidence interval = 95%

Using 2)95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

μ – 2σ

= 349 - 2(24)

= 349 - 48

= 301

μ + 2σ

349 + 2(24)

= 349 + 48

= 397

Therefore, according to the standard deviation rule, approximately 95% of the students spent between $301 and $397 on textbooks in a semester.

8 0

3 years ago

A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the

hichkok12 [17]

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that $p = 0.08$

Sample of 595:

This means that $n = 595$

Mean and standard deviation:

$\mu = p = 0.08$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111$

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

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

By the Central Limit Theorem

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

$Z = \frac{0.05 - 0.08}{0.0111}$

$Z = -2.7$

$Z = -2.7$ has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

8 0

3 years ago

An amusement park would like to determine if they want to add in a new roller coaster. In order to decide whether or not they sh

Rzqust [24]

Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 90% confidence level, hence $\alpha = 0.9$ , z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$ , so the critical value is z = 1.645.

The sample size and the estimate are given by:

$n = 600, \pi = \frac{400}{600} = 0.6667$

Hence, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 - 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6350$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6667 + 1.645\sqrt{\frac{0.6667(0.3333)}{600}} = 0.6984$

The 90% confidence interval is given by: (0.6350, 0.6984).

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

5 0

2 years ago

Mai says that -8 > -4 . Do you agree with her? Explain or show your reasoning.

Elza [17]

Answer:

No

Step-by-step explanation:

-8 is less than -4. Negative numbers reverse the logic of positive ones: since positive 8 is more than positive 4, negative 8 is less than negative 4.

7 0

3 years ago

Aanand earns Rs 80 in 7 hours and pramode earns Rs 90 in 12 hours. find their ratio​

Aanand earns Rs 80 in 7 hours and pramode earns Rs 90 in 12 hours. find their ratio