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omeli [17]
3 years ago
10

Phillip and Ryan are saving money for college. Phillip started with $500 in his savings account and saves $25 a week. Ryan start

ed with $250 in his savings account and saves $25 a week. If they continue at the same rate, will Phillip and Ryan ever have the same amount of money in their savings accounts?
Mathematics
2 answers:
hoa [83]3 years ago
6 0
No they will never have the same amount of money in their bank accounts because Phillip started with $250 more then Ryan and if they both put $25 in every week then Phillip's money will always be $250 more then Ryan's
Amanda [17]3 years ago
5 0
I don't think so because Phillip has more to begin with and they are saving the same amount at the same rate. So unless Philip stops saving then Ryan will not catch up.

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Of the total population of the United States, 20% live in the northeast. If 200 residents of the United States are selected at r
Snezhnost [94]

Answer:

0.0465 = 4.65% probability that at least 50 live in the northeast.

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 200, p = 0.2

So

\mu = E(X) = np = 200*0.2 = 40

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.65685

Approximate the probability that at least 50 live in the northeast.

Using continuity correction, this is P(X \geq 50 - 0.5) = P(X \geq 49.5, which is 1 subtracted by the pvalue of Z when X = 49.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{49.5 - 40}{5.65685}

Z = 1.68

Z = 1.68 has a pvalue of 0.9535

1 - 0.9535 = 0.0465

0.0465 = 4.65% probability that at least 50 live in the northeast.

3 0
3 years ago
How do i find the estimate of 92×68 please help!!!!!!!
Gnesinka [82]
It's 6256 as the answer.So I would put it as 6250
6 0
3 years ago
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