Luis, Marlon, and Victoria are counting money. They each have the same amount in dollar bills, quarters, dimes, nickels, and pen
2 answers:
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Option A
The solution is
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
3x + 6y = 1 ------ eqn 1
x - 4y = 1 ------ eqn 2
We have to find solution to system of equations
We can use substitution method
From eqn 2,
x = 1 + 4y -------- eqn 3
Substitute eqn 3 in eqn 1
3(1 + 4y) + 6y = 1
3 + 12y + 6y = 1
18y = 1 - 3
18y = -2
Divide both sides by 18
Substitute the above value of y in eqn 3
Thus solution is
Answer:
Probability that their mean height is less than 68 inches is 0.0764.
Step-by-step explanation:
We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.
Also, 16 men are randomly selected.
<em>Let </em><em> = sample mean height</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean height = 69 inches
= population standard deviation = 2.8 inches
n = sample of men = 16
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P( < 68 inches)
P( < 68 inches) = P(
<
) = P(Z < -1.43) = 1 - P(Z
1.43)
= 1 - 0.9236 = 0.0764
<em>Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.</em>
Therefore, probability that their mean height is less than 68 inches is 0.0764.