Answer:
a.0.8664
b. 0.23753
c. 0.15866
Step-by-step explanation:
The comptroller takes a random sample of 36 of the account balances and calculates the standard deviation to be N42.00. If the actual mean (1) of the account balances is N175.00, what is the probability that the sample mean would be between
a. N164.50 and N185.50?
b. greater than N180.00?
c. less than N168.00?
We solve the above question using z score formula
z = (x-μ)/σ/√n where
x is the raw score,
μ is the population mean = N175
σ is the population standard deviation = N42
n is random number of sample = 36
a. Between N164.50 and N185.50?
For x = N 164.50
z = 164.50 - 175/42 /√36
z = -1.5
Probability value from Z-Table:
P(x = 164.50) = 0.066807
For x = N185.50
z = 185.50 - 175/42 /√36
z =1.5
Probability value from Z-Table:
P(x=185.50) = 0.93319
Hence:
P(x = 185.50) - P(x =164.50)
= 0.93319 - 0.066807
= 0.866383
Approximately = 0.8664
b. greater than N180.00?
x > N 180
Hence:
z = 180 - 175/42 /√36
z = 5/42/6
z = 5/7
= 0.71429
Probability value from Z-Table:
P(x<180) = 0.76247
P(x>180) = 1 - P(x<180) = 0.23753
c. less than N168.00?
x < N168.
z = 168 - 175/42 /√36
z = -7/42/6
z = -7/7
z = -1
Probability value from Z-Table:
P(x<168) = 0.15866
Let, the cost of a belt = x
cost of a wallet = y
Then, system of equations would be:
x + y = 42
7x + 4y = 213
Multiply 1st equation by 4,
4x + 4y = 168
Substitute it from 2nd equation,
3x = 45
x = 15
Now, substitute it in 1st equation,
15 + y = 42
y = 42 - 15 = 27
In short, Belt costs $15 and wallet costs $27
Hope this helps!
Answer: choice D
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Work Shown:
I'm assuming the problem is -4*(1-x) <= -12+2x where the first term is -4 and not 4
-4*(1-x) <= -12+2x
-4*(1-x) <= -12+2x
-4+4x <= -12+2x
-4+4x-2x <= -12+2x-2x
-4+2x <= -12
-4+2x+4 <= -12+4
2x <= -8
2x/2 <= -8/2
x <= -4
To graph x <= -4, you plot a closed circle at -4. Then you shade to the left of the closed circle. This matches with choice D
Answer:
4 inches
Step-by-step explanation:
The computation of the scale that should be required to reproduced that fitted on the brochure is
Given that
Length of rectangular park = 4 inches
And the Breadth of rectangular park = 6 inches
As we know that
Area of rectangular park = length × breadth
= 4×6
= 24 square inches
Now the scale that required to reproduced is
= 24 ÷ 6
= 4 inches
Answer:
2/9 = 0.22
Step-by-step explanation:
There are two ways to pick the first number odd and less than 5: 1 and 3.
With each of these, the second number drawn can be 1, 2, 3, 4, 5, 6, 7, 8 or 9.
This makes 18 total possibilities.
Out of these, the only ways to have a sum less than 5 are 1 and 1, 1 and 2, 1 and 3, and 3 and 1. This is 4 ways out of 18:
4/18 = 2/9 = 0.22