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Assume that X is Normal with mean $ 240 and standard deviation $60 . the probability that , in a randomly selected week , Dan will make less than $ 255

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Answer:

The probability of Dan making less than $255 is 0.5987 or 59.87%

Step-by-step explanation:

Given that:

Mean = μ = $240

SD = σ = $60

We have to find the probability that Dan will make less than $255

First of all, we have to find the z-score of 255

z-score is denoted by z and is given by the formula

[tex]z = \frac{x-mean}{SD}[/tex]

Here,

x = 255

Putting the values

[tex]z = \frac{255-240}{60}\\z = \frac{15}{60}\\z = 0.25[/tex]

Now we have to look at the z-score table to find the probability of 0.25

P(x<255) = 0.5987

Converting into percentage

59.87%

Hence,

The probability of Dan making less than $255 is 0.5987 or 59.87%

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