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3 years ago

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Kyle has $1 comma 000 in cash received for high school graduation gifts from various relatives. He wants to invest it in a cert

ificate of deposit (CD) so that he will have a down payment on a car when he graduates from college in five years. His bank will pay 1.5% per year, compounded annually, for the five-year CD. How much will Kyle have in five years to put down on his car?

1 answer:

Vera_Pavlovna [14]3 years ago

4 0

Answer:

$1077.283

Step-by-step explanation:

When complete the first year the amount will be:

1000 * 1.015= 1015

1.015 because the rate is added to the initial amount, that is: 100%+1.5% = 1 + 0.015= 1.015

When complete the second year the amount will be the last year amount adding the rate interest:

1015*1.015=1030.225.

To the third year:

1030.225*1.015=1045.678

To the fourth year:

1045.678*1.015=1061.363

To the fifth year:

1061.363*1.015=1077.283

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Suppose you are working in an insurance company as a statistician. Your manager asked you to check police records of car acciden

pochemuha

Answer:

(a) 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We conclude that the the percentage of teenagers has not changed since you join the company.

(d) We conclude that the the percentage of teenagers has changed since you join the company.

Step-by-step explanation:

We are given that your manager asked you to check police records of car accidents and out of 576 accidents you selected randomly, teenagers were at the wheel in 120 of them.

(a) Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

where, $\hat p$ = sample proportion teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

p = population percentage of all car accidents

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population population, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ) = 0.95

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ]

= [ $0.21-1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ , $0.21+1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ ]

= [0.177 , 0.243]

Therefore, 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We are also provided that before you were hired in the company, the percentage of teenagers who where involved in car accidents was 18%.

The manager wants to see if the percentage of teenagers has changed since you join the company.

<u><em>Let p = percentage of teenagers who where involved in car accidents</em></u>

So, Null Hypothesis, $H_0$ : p = 18% {means that the percentage of teenagers has not changed since you join the company}

Alternate Hypothesis, $H_A$ : p $\neq$ 18% {means that the percentage of teenagers has changed since you join the company}

The test statistics that will be used here is <u>One-sample z proportion statistics</u>;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} }}$ ~ N(0,1)

where, $\hat p$ = sample proportion teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

So, <u><em>test statistics</em></u> = $\frac{0.21-0.18}{\sqrt{\frac{0.21(1-0.21)}{576} }}$

= 1.768

The value of the sample test statistics is 1.768.

Now at 0.05 significance level, the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the the percentage of teenagers has not changed since you join the company.

(d) Now at 0.1 significance level, the z table gives critical value of -1.6449 and 1.6449 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that the the percentage of teenagers has changed since you join the company.

4 0

3 years ago

Which is the simplified form of the expression 3(7/5x+4) - 2(3/2 - 5/4x)?

Kruka [31]

Answer:

B. $\frac{67}{10} x + 9$

Step-by-step explanation:

Simplify the expression. Remember to go by the order of operations, or PEMDAS.

1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

$3(\frac{7}{5} x + 4) -2 (\frac{3}{2} -\frac{5}{4} x)$

$\frac{21}{5}x + 12 - \frac{6}{2} + \frac{10}{4} x$

$\frac{21}{5} x + 12 - 3 + \frac{10}{4} x$

2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

$\frac{21}{5} x + 9 + \frac{10}{4}x \\\frac{84}{20}x + \frac{50}{20}x + 9 \\\frac{134}{20}x + 9 \\\frac{67}{10}x + 9$

Thus, the answer is $\frac{67}{10} x + 9$ .

8 0

3 years ago

What is 8blank7 hundred divided by 4 equal

Gnoma [55]

$\frac{870}{4} = \frac{435}{2} 
$

<span>(Decimal: 217.5)
</span>
For if its
$\frac{8700}{4}$

Then is $=2175$

~ Hope this helps

3 0

3 years ago

Plz Help .............

Rus_ich [418]

$363.9ft^{2}$

Step-by-step explanation:

$Area =\pi r^{2} -\frac{1}{3}\pi r^{2} +\frac{1}{2}r^{2}sin\alpha \\\\\\ = \frac{2}{3}\pi 12^{2} +\frac{1}{2}12^{2}sin120 =363.9ft^{2}$

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Ksju [112]

Answer:

C

Step-by-step explanation:

4 0

3 years ago