Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year. If no deposits or withdrawals are made during the year, how much money will be in her account after one year?

FV= $1,545

Step-by-step explanation:

Giving the following information:

Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year.

To calculate the nominal value of the account after one year, we need to use the following formula:

FV= (P*r*t) + P

FV= future value

P= principal

r= interest rate

t= 1

FV= (1,500*0.03*1) + 1,500

FV= $1,545

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

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 and standard deviation , the z-score of a measure X is given by:

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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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 and standard deviation

Suppose 46% of politicians are lawyers.

This means that

Sample of size 662

This means that

Mean and standard deviation:

What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?

p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So

X = 0.5

By the Central Limit Theorem

has a p-value of 0.9803

X = 0.42

has a p-value of 0.0197

0.9803 - 0.0197 = 0.9606

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%