A hotel has $4,695 to buy new pillows. If the cost of each pillow is $5, how many pillows will the hotel be able to buy?
2 answers:
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Answer:
5.3 or 28
Step-by-step explanation:
+
=
36+=64
64-36=28
=5.29 or 5.3
Using the normal distribution, it is found that there was a 0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
The probability of a month having a PCE between $575 and $790 is the <u>p-value of Z when X = 790 subtracted by the p-value of Z when X = 575</u>, hence:
X = 790:
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
X = 575:
Z = -2.5
Z = -2.5 has a p-value of 0.0062.
0.9641 - 0.0062 = 0.9579.
0.9579 = 95.79% probability of a month having a PCE between $575 and $790.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
(a) P(x) = 300 x - 3600
(b) P(340) = $ 98400
(c) At least 12 items must be sold to avoid losing money.
Step-by-step explanation:
Part (a):
The Profit function is the difference between the revenue function (R(x)) and the Cost (C(x)) function:
P(x) = R(x) - C(x)
P(x) = 384 x - [84 x + 3600]
P(x) = 384 x - 84 x - 3600
P(x) = 300 x - 3600
Part (b):
The profit on 340 items is:
P(340) = 300 (340) - 3600
P(340) = 102000 - 3600
P(340) = $ 98400
Part (c):
To avoid losing money, the profit P(x) has to be larger or equal than zero. That is:
P(x) 0
300 x -3600 0
300 x 3600
x 3600/300
x 12
So at least 12 items must be sold to avoid losing money.