In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes. For a simple haircut, the middle 90 percent of the customers will require:a) between 20.0 and 30.0 minutes. b) between 18.4 and 31.6 minutes. c) between 17.2 and 32.8 minutes. d) between 19.9 and 30.1 minutes.

For a simple haircut, the middle 90 percent of the customers will require between 18.4 and 31.6 minutes.

So, Option (b) is correct.

Normal distribution is a continuous probability distribution where values lie in a symmetrical fashion mostly situated around the mean.

Here, we use Z score rule in normally distribution.

Let us assume that mean is and standard deviation is and X is measure of variable.

So,      

Given that, mean = 25 and deviation = 4

Now we have to find lower bound value of variable X when Z = -1.645

Now we have to find upper bound value of variable X when Z = 1.645

Since, value of variable X  is between 18.42 and 31.58.

Therefore, For a simple haircut, the middle 90 percent of the customers will require between 18.4 and 31.6 minutes.

Thus, option (b) is correct.

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b) between 18.4 and 31.6 minutes.

Step-by-step explanation:

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

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

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:

Middle 90%

Lower bound: Value of X when Z has a pvalue of 0.5 - 0.9/2 = 0.05.

Upper bound: Value of X when Z has a pvalue of 0.5 + 0.9/2 = 0.95.

Lower bound:

X when Z = -1.645

Upper bound

X when Z = 1.645

So the correct answer is:

b) between 18.4 and 31.6 minutes.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

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