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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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I don't know for sure, but I think the answer is 200

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2 years ago
Mason has a collection of 49¢ stamps, 20¢ stamps, and 34 stamps worth $23.55. He has 56 total 49¢ and 20+ stamps and the number
tatuchka [14]

Answer:

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.

Step-by-step explanation:

Let x be the number of 20¢ stamps, then the number of 3¢ stamps is  x + 9.

Mason has 56 total 49¢ and 20¢ stamps, then the number of 49¢ stamps is 56 - x.

Amounts:

  • in 49¢: 49(56-x) cents;
  • in 20¢: 20x cents;
  • in 3¢: 3(x+9) cents.

Total amount:

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Hence,

49(56-x)+20x+3(x+9)=2,355\\ \\2,744-49x+20x+3x+27=2,355\\ \\-49x+3x+20x=2,355-2,744-27\\ \\-26x=-416\\ \\26x=416\\ \\x=16

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.
5 0
3 years ago
Total of 589 tickets were sold for the school play. they were either adult tickets or student tickets. there were 61 fewer stude
olga_2 [115]
A+S=589
S=a-61
A+A-61=589
2a=589+61
2a=650
A=325
S=325-61
S=264
Hope this helps
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</span><span><span>I hope this helped! Please take the time to rate, pick the Brainliest answer (not necessarily mine!), and thank me if you feel I helped with this question! Thank you, it helps me a lot. :)</span></span>
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the area of a roof on a house is n756 square inches. the length of the roof is 108 inches. how many inches wide is the roof?
Leno4ka [110]
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So Width = Area/Length = 756/108 = 7 inches wide</span><span>
</span>
6 0
3 years ago
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