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makkiz [27]
3 years ago
7

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.

Mathematics
1 answer:
Alona [7]3 years ago
4 0

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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Hal has a steel barrel with a diameter of 6 feet that can be filled to a depth of 4.6 feet with oil. What is the volume of the b
scoray [572]

Answer:

129.996 cubic feet

Step-by-step explanation:

Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

\pi(r)^2(h)

First, we have to find the radius, which is:

D = 2r

So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.

3.14(3)^2(4.6)

Now, we solve. Exponents are first...

3.14(9)(4.6)

Now multiply left to right.

28.26(4.6)

129.996 cubic feet

Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!

3 0
3 years ago
Fwd:The hardware store is having a 15% off sale on lawn mowers this weekend. If x is the original price of a lawn mower, what wi
Sveta_85 [38]

Answer:

<h3>(x - 0.15x) and x(1.00 - 0.15)</h3>

Step-by-step explanation:

Let x be the original price of a lawn mower,

If the hardware store is having a 15% off sale on lawn mowers this weekend, the amount discounted is expressed as;

= 15 % of x

= 0.15 of x

= 0.15x

Final sales price = Original price - discounted price;

Final sales price = x - 0.15x

Factor out x;

x - 0.15x = x(1 - 0.15)

Hence the correct equations are (x - 0.15x)  and x(1.00 - 0.15)

3 0
2 years ago
What are the domain and<br> range of the function below?
Olin [163]

Answer:

2nd answer option

Step-by-step explanation:

the domain is the interval or set of valid x values. the range is the same for valid y values.

so, what is the smallest x value we see in the functional graph ?

x = 0

there is no functional value for any x smaller than that.

and then the function goes on and on to the right in all eternity. that means it goes to infinity.

so, domain = [0, infinity)

please consider the round bracket at the end, because "infinity" is not a number.

now for the range and the y values.

in this case I start to ask for the largest y value.

y = 4

for no x value do we get a larger y value.

but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).

so, the range = (-infinity, 4]

"-infinity" is also not a number and therefore not included (hence the round bracket).

5 0
1 year ago
determine if it can be proven that the triangles are congruent if they are the choose a theorem that proves its congruent ​
Lostsunrise [7]

Answer:

These triangles are congruent by SAS

Step-by-step explanation:

They share the same angle which is in the same angle which is the vertical angle with congruent sides on either side of the angle, therefore this is congruent by SAS.

7 0
3 years ago
An exam has two probability problems, 1 and 2. If 37% of the students solved problem 1 and 12% of the students solved both probl
yan [13]

Answer:

63%

Step-by-step explanation:

37% did not solve problem 2

100% - 37% = 63%

3 0
3 years ago
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