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daser333 [38]
3 years ago
12

The number of gallons of carbonated soft drink consumed per person annually is normally distributed with mean 47.5 and standard

deviation 3.5.The probability that a randomly selected person consumes between 45 and 50 gallons of carbonated soft drink per year is about:
Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

Answer:

P(45

And we can find this probability with the following difference:

P(-0.714

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-0.714

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 number of gallons of a population, and for this case we know the distribution for X is given by:

X \sim N(47.5,3.5)  

Where \mu=47.5 and \sigma=3.5

We are interested on this probability

P(45

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(45

And we can find this probability with the following difference:

P(-0.714

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-0.714

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3 years ago
5. What's true of the distribution of any variable, if your model is the mean of that variable? A The distribution of the variab
Alex

The true statement about the distribution of any variable model around the mean is (D) The distribution of the variable is the same shape as the distribution of its residual

<h3>The true statement about the distribution</h3>

From the question, we understand that the distribution of the model is based on its mean or average value.

The above means that the upper and the lower deviations are balanced.

Hence, the true statement about the distribution of any variable model around the mean is (D)

Read more about distribution at:

brainly.com/question/15713806

6 0
2 years ago
PLEASE HELP HURRY!!!!!!!!!
Rzqust [24]

Answer:

PC = 14.42 cm

Step-by-step explanation:

If a tangent and secant are drawn from a point outside a circle, then the product of the lengths of the segments of the secant is equal to the square of the length of the tangent.

PC² = PB × BD

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6 0
3 years ago
When constructing inscribed polygons and parallel lines, how are the steps similar?
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3 years ago
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What power of 10 is used to write the number
Anastasy [175]

Answer: Seventh power of 10


Step-by-step explanation:

X > 1 so exponent will be positive and decimal point moves left. At each point divide X by 10, add 1 to exponent of 10. Exponent starts at zero.


Each time you move the decimal point one to left, you have divided the number by 10, so you have to compensate by multiplying the 10^n factor by 10, say 10 × 10^3 = 10×10×10×10 = 10^4.


12345678 = 12345678 × 10^0

= 1234567.8 × 10^1

= 123456.78 × 10^2

= 12345.678 × 10^3

= 1234.5678 × 10^4

= 123.45678 × 10^5

= 12.345678 × 10^6

= 1.2345678 × 10^7


Each time you move decimal to right, you have multiplied the number by 10, so you have to compensate by dividing the 10^n by 10, subtracting one from exponent.


0.000123 × 10^0 = 0.00123 × 10^-1

= 0.0123 × 10^-2 = 0.123 × 10^-3 = 1.23 × 10^-4


10^-2 / 10 = (1/(10×10)) / 10 = 1/(10×10×10) = 10^-3

6 0
3 years ago
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