Mathematics, 02.03.2020 23:28, carlyfaith3375

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.

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answered: belmontes

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 $\mu$ and standard deviation is $\sigma$ and X is measure of variable.

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

Given that, mean = 25 and deviation = 4

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

$-1.645=\frac{X-25}{4}\\\\X=18.42$

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

$1.645=\frac{X-25}{4}\\\\X=31.58$

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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answered: brevancci

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 $\mu$ 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:

$\mu = 25, \sigma = 4$

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

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

$-1.645 = \frac{X - 25}{4}$

X - 25 = -1.645*4

X = 18.42

Upper bound

X when Z = 1.645

$1.645 = \frac{X - 25}{4}$

X - 25 = 1.645*4

X = 31.58

So the correct answer is:

b) between 18.4 and 31.6 minutes.

answered: Guest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

answered: Guest

m=-16

step-by-step explanation: