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Explanation & Answer
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1.
QUIZ 2
The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3
minutes and a standard deviation of 2 minute.
a. What proportion of bank customers waits between 3 and 4 minutes
𝑃(3 ≤ 𝑥 ≤ 4) = 𝑃(𝑥 ≤ 4) − 𝑃(𝑥 ≤ 3)
4−3
3−3
𝑃(3 ≤ 𝑥 ≤ 4) = 𝑃 (𝑧 ≤
) − 𝑃 (𝑧 ≤
)
2
2
𝑃(3 ≤ 𝑥 ≤ 4) = 𝑃(𝑧 ≤ 0.5) − 𝑃(𝑧 ≤ 0)
𝑃(3 ≤ 𝑥 ≤ 4) = 0.6915 − 0.5
𝑃(3 ≤ 𝑥 ≤ 4) = 𝟎. 𝟏𝟗𝟏𝟓
b. What percentage wait more than 4 minutes?
𝑃(𝑥 ≥ 4) = 1 − 𝑃(𝑥 ≤ 4)
4−3
𝑃(𝑥 ≥ 4) = 1 − 𝑃 (𝑧 <
)
2
𝑃(𝑥 ≥ 4) = 1 − 𝑃(𝑧 < 0.5)
Using a z-score table we find the probabilities for z = 0.5
𝑃(𝑥 ≥ 4) = 1 − 0.6915
𝑃(𝑥 ≥ 4) = 0.3085
This is ...