If £2000 is placed into a bank account that pays 3% compound interest per year, how much will be in the bank account after 2 yea
1 answer:
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Answer:
$42,890
Step-by-step explanation:
The standard form for an exponential equation is
where a is the initial amount value and b is the growth rate or decay rate and t is the time in years. Since we are dealing with money amounts AND this is a decay problem, we can rewrite accordingly:
where A(t) is the amount after the depreciation occurs, r is the interest rate in decimal form, and t is the time in years. We know the initial amount (70,000) and the interest rate (.04), but we need to figure out what t is. If the car was bought in 2006 and we want its value in 2018, a total o 12 years has gone by. Therefore, our equation becomes:
or, after some simplification:
First rais .96 to the 12th power to get
A(t) = 70,000(.6127097573)
and then multiply.
A(t) = $42,890
Answer:
The probability that the sample mean would differ from the population mean by more than 0.5 millimeters is 0.2420.
Step-by-step explanation:
Let <em>X</em> = the diameter of the steel bolts manufactured by the steel bolts manufacturing company Thompson and Thompson.
The mean diameter of the bolts is:
<em>μ</em> = 149 mm.
The standard deviation of the diameter of bolts is:
<em>σ</em> = 5 mm.
A random sample, of size <em>n</em> = 49, of steel bolts are selected.
The population of the diameter of bolts is not known.
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
The mean of the sampling distribution of sample mean is:
The standard deviation of the sampling distribution of sample mean is:
Compute the probability that the sample mean would differ from the population mean by more than 0.5 millimeters as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by more than 0.5 millimeters is 0.2420.