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marin [14]
3 years ago
13

The distribution of the number of transactions performed at a bank each day is approximately normal with mean 478 transactions a

nd standard deviation 64 transactions. Which of the following is closest to the proportion of daily transactions greater than 350?
a. 0.023
b. 0.046
c. 0.954
d. 0.477
e. 0.977
Mathematics
1 answer:
jolli1 [7]3 years ago
6 0

Answer:

e. 0.977

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

\mu = 478, \sigma = 64

Which of the following is closest to the proportion of daily transactions greater than 350?

This is 1 subtracted by the pvalue of Z when X = 350. So

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

Z = \frac{350 - 478}{64}

Z = -2

Z = -2 has a pvalue of 0.023

1 - 0.023 = 0.977

So the correct answer is:

e. 0.977

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