A banks loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviati
on of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 21.5.
1 answer:
Answer:
2.87%
Step-by-step explanation:
We have the following information:
mean (m) = 200
standard deviation (sd) = 50
sample size = n = 40
the probability that their mean is above 21.5 is determined as follows:
P (x> 21.5) = P [(x - m) / (sd / n ^ (1/2))> (21.5 - 200) / (50/40 ^ (1/2))]
P (x> 21.5) = P (z> -22.57)
this value is very strange, therefore I suggest that it is not 21.5 but 215, therefore it would be:
P (x> 215) = P [(x - m) / (sd / n ^ (1/2))> (215 - 200) / (50/40 ^ (1/2))]
P (x> 215) = P (z> 1.897)
P (x> 215) = 1 - P (z <1.897)
We look for this value in the attached table of z and we have to:
P (x> 215) = 1 - 0.9713 (attached table)
P (x> 215) =.0287
Therefore the probability is approximately 2.87%
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Answer:
1. <u>Cost per customer</u>: 10 + x
<u>Average number of customers</u>: 16 - 2x
3. $10, $11, $12 and $13
Step-by-step explanation:
<u>Given information</u>:
- $10 = cost of buffet per customer
- 16 customers choose the buffet per hour
- Every $1 increase in the cost of the buffet = loss of 2 customers per hour
- $130 = minimum revenue needed per hour
Let x = the number of $1 increases in the cost of the buffet
<u>Part 1</u>
<u></u>
<u>Cost per customer</u>: 10 + x
<u>Average number of customers</u>: 16 - 2x
<u>Part 2</u>
The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130. Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:
<u>Part 3</u>
To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:
Find the roots by equating to zero:
Therefore, the roots are x = 3 and x = -5.
<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:
As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:
-5 ≤ x ≤ 3
To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.
[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]
<u>Cost per customer</u>:
Therefore, the possible buffet prices Noah could charge are:
$10, $11, $12 and $13.