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normally distributed with mean 24.6 seconds and standard deviation 0.64 seconds;the lower finishing time, the better. If the qua

marshall27 [118]

Answer:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the finishing time of a population, and for this case we know the distribution for X is given by:

$X \sim N(24.6,0.64)$

Where $\mu=24.6$ and $\sigma=0.64$

Solution to the problem

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.15$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

3 0

2 years ago

An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest

vitfil [10]

Exponential decay is a very common process especially when we are talking about radioactive materials. So, there is already a common formula for this type of behavior which is written below:

A = Pe^-rt
where
A is the amount left after time t
P is the initial amount at t=0
r is the rate

Substituting the values,
A = (780 g)(e^-0.163*16)
A = 57.5 g

8 0

3 years ago

A man purchased a magazine at the airport for $2.69. The tax on the purchase was $0.13. What is the tax rate at the airport? The

alexdok [17]

We need to find the percent, let's start but making the equation.

The price is 2.69

The tax cost is 0.13

So what percent of 2.69 is = 0.13.

Equation: X/100 x 2.69 = 0.13

Multiply each side by 100 so we can get x alone with the price: 2.69x = 13

Now to get x alone, we must divide both sides by 2.69: x = 4.8

Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.

I hope this helps! :)

6 0

3 years ago

Three people build a rectangular shed 8 ft wide, 6 ft long, and 7 ft high. How many cubic feet does the shed contain?

dusya [7]

8x6x7= 336
Your answer is 336 ft^3

7 0

3 years ago

While shopping, janet bought a shirt for $8, a pair of jeans for $22, mittens for $5, and a hat for $10. how much money did jane

Talja [164]

Janet spent $45 in all

5 0

3 years ago