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3 years ago

If the interest earned on an account after 7 years at 6% is $1785 ,what is the initial value

Mathematics

1 answer:

gayaneshka [121]3 years ago

8 0

Answer:

$4250

Step-by-step explanation:

i = prt

p = i / rt

where,

i = $1,785

r = 6% = 0.06

t = 7 years

So, we can calculate initial vale by putting the values in above equation;

p = $1,785 / (0.06 x 7)

p = $1,785 / 0.42

p = $4,250

Hence the initial value will be $4250

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Answer:

a) n =1623

b) $ME=2.0538\sqrt{\frac{0.21 (1-0.21)}{1623}}=0.0208$

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken

$\hat p=0.19$ estimated proportion of customers are not satisfied with the service provided by the local dealer

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Me= 0.02 represent the margin of error

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 96% of confidence, our significance level would be given by $\alpha=1-0.96=0.04$ and $\alpha/2 =0.02$ . And the critical value would be given by: