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olga_2 [115]
3 years ago
8

Based on historical data, your manager believes that 40% of the company's orders come from first-time customers. A random sample

of 91 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.26 and 0.43? Answer = (Enter your answer as a number accurate to 4 decimal places.)
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
7 0

Answer:

P(0.26 \leq p \leq 0.43)=0.7204-0.0032=0.7172

Step-by-step explanation:

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".  

The population proportion have the following distribution

p \sim N(p=0.4,\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.4(1-0.4)}{91}}=0.0514)

And we can solve the problem using the z score on this case given by:

z=\frac{p_o -p}{\sqrt{\frac{p(1-p)}{n}}}

We are interested on this probability:

P(0.26 \leq p \leq 0.43)

And we can use the z score formula, and we got this:

P(\frac{0.26 -0.4}{\sqrt{\frac{0.4(1-0.4)}{91}}} \leq Z \leq \frac{0.43 -0.4}{\sqrt{\frac{0.4(1-0.4)}{91}}})

P(-2.726 \leq Z \leq 0.584)

And we can find this probability like this:

P(-2.726 \leq Z \leq 0.584)=P(Z

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Step-by-step explanation:

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4 years ago
Angie divides the polynomial function f(x)=x3+3x2−7x−21 by (x + 3). What can she conclude from the fact that the remainder is eq
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Answer:

See below

Step-by-step explanation:

<u>Given function</u>

  • f(x)=x³ + 3x²- 7x - 21

<u>We can find its factors:</u>

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We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)

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8 0
3 years ago
Please help<br> c=x+b solve for x
fredd [130]

Answer:

x = c - b

Step-by-step explanation:

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Answer:

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Step-by-step explanation: this is the same paragraph The square root of π has attracted attention for almost as long as π itself. When you’re an ancient Greek mathematician studying circles and squares and playing with straightedges and compasses, it’s natural to try to find a circle and a square that have the same area. If you start with the circle and try to find the square, that’s called squaring the circle. If your circle has radius r=1, then its area is πr2 = π, so a square with side-length s has the same area as your circle if s2  = π, that is, if s = sqrt(π). It’s well-known that squaring the circle is impossible in the sense that, if you use the classic Greek tools in the classic Greek manner, you can’t construct a square whose side-length is sqrt(π) (even though you can approximate it as closely as you like); see David Richeson’s new book listed in the References for lots more details about this. But what’s less well-known is that there are (at least!) two other places in mathematics where the square root of π crops up: an infinite product that on its surface makes no sense, and a calculus problem that you can use a surface to solve.

5 0
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