Mathematics, 26.06.2020 15:01 picklespicklesdicc

A recent survey found that about 72.5% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 300 gasoline purchases completed at this chain are randomly selected, find the probability that at most 210 of those purchases are paid with a credit or debit card.

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Answer from: henbry540

18.28% probability that at most 210 of those purchases are paid with a credit or debit card.

Step-by-step explanation:

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 = 300, p = 0.725

$\mu = E(X) = np = 300*0.725 = 217.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.725*0.275} = 7.7339$

Find the probability that at most 210 of those purchases are paid with a credit or debit card.

Using continuity correction, this is $P(X \leq 210 + 0.5) = P(X \leq 210.5)$ , which is 1 subtracted by the pvalue of Z when X = 210.5. So

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

$Z = \frac{210.5 - 217.5}{7.7339}$

Z = -0.905

Z = -0.905 has a pvalue of 0.1828

18.28% probability that at most 210 of those purchases are paid with a credit or debit card.

Answer from: Quest

answer

see attachment

explanation

the given function is

$y = 2x - 4$

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

Answer from: Quest

$79500

step-by-step explanation:

75000÷100=750750×106=79500

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