Assume that the weights of individuals are independent and normally distributed with a mean of 160 pounds and a standard deviation of 30 pounds. suppose that 25 people squeeze into an elevator designed to hold 4300 pounds.
a)what is the probability that the total weight exceeds the design limit
b)what design limit is exceeded by 25 occupants with probability .0001?

a)

b) 3,624.25 pounds

Step-by-step explanation:

a)

Since 4300/25 = 172, in average every single person should weight 172 pounds to exceed the design limit.

The probability that one person weights 172 pounds or more is the area under the Normal curve with mean 160 pounds and standard deviation 30 pounds to the right of 172.

In Excel and OpenOffice Calc, this value is found with the formula

=1-NORMDIST(172;160;30;1)

(NORMDIST(172;160;30;1) gives the area to the left of 172, so 1-NORMDIST(172;160;30;1) gives the area to the right of 172)

and equals 0.3446

(see picture 1)

Hence, the probability that all the 25 people exceeds 172 pounds equals

b)

Similarly, we must find a weight w such that if p is the area to the left of w, then  

so  

w would be the point such that the area under the Normal curve with mean 160 pounds and standard deviation 30 pounds to the right of w equals 0.6918.

In Excel and OpenOffice Calc this is found with

=NORMINV(1-0.6918;160;30)

and equals 144.97 pounds

(See picture 2)

and the design limit that is exceeded by 25 occupants with probability 0.0001 is 25*144.97 = 3,624.25 pounds

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204