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yan [13]
3 years ago
10

Andrei's grandfather offered to give him a gift at 50% of the amount of money he saved in one year. Andrei saved $120 dollars. H

ow much did his grandfather give him as a gift?
Mathematics
2 answers:
Dafna1 [17]3 years ago
3 0

Answer:

$60

Step-by-step explanation:

$120/2(half) = $60

Harman [31]3 years ago
3 0

Answer: The amount given by his grandfather to him = $60.

Step-by-step explanation:

Given : Andrei's grandfather offered to give him a gift at 50% of the amount of money he saved in one year.

The amount saved by Andrei = $ 120

Then, the amount given by his grandfather to him will be

50% of ( amount saved by Andrei )

= (0.50) x ($120) [When we convert a percent into decimal we divide it by 100]

= $60

Therefore , the amount given by his grandfather to him = $60.

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Make a box ­and ­whisker plot of the data.<br><br> 24, 18, 29, 21, 16, 23, 13, 11
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To make a box and whisker plot you must first order the data:

11, 13, 16, 18, 21, 23, 24, 29

Then find the median:

19.5

Then split the data into two sections by the median:

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Now find the medians of those sets

14.5 and 23.5

With this information we can conclude Option C is the correct plot

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At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul
vampirchik [111]

Answer:

a) Null Hypothesis: \mu =900

Alternative hypothesis: \mu \neq 900

b) The 95% confidence interval would be given by (910.05;959.95)    

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750

Since is a bilateral test the p value is given by:

p_v =2*P(Z>2.750)=0.0059

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: \mu =900

Alternative hypothesis: \mu \neq 900

b. What is the 95% confidence interval estimate of the population mean examination  score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

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".

\bar X=935 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=180 represent the population standard deviation

n=200 represent the sample size  

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=3278.222

The sample deviation calculated s=97.054

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

935-1.96\frac{180}{\sqrt{200}}=910.05    

935+1.96\frac{180}{\sqrt{200}}=959.95    

So on this case the 95% confidence interval would be given by (910.05;959.95)    

c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your  conclusion?

Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

The statistic is given by:

z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

If we replace we got:

z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750

Since is a bilateral test the p value is given by:

p_v =2*P(Z>2.750)=0.0059

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

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Answer:

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Step-by-step explanation:

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Answer:

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Hope this answer is right!!

Step-by-step explanation:

Length be 3 cm longer than the breadth.

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So, x+y=27 =>x=15

x-y=3 =>x=12

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