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11111nata11111 [884]
3 years ago
9

Mel's Movie House prepares popcorn for 30% more people than the expected attendance at the movies each day. How many people shou

ld Mel prepare popcorn for, to plan for 850 movie-goers?​
Mathematics
1 answer:
Bond [772]3 years ago
8 0
1,105

850 x .30 = 255
850 + 255 = 1,105
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According to the last census (2010), the mean number of people per household in the United States is LaTeX: \mu = 2.58 Assume a
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Answer:

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, \mu = 2.58 and Standard deviation, \sigma = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

             Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar \leq 2.50)

P(Xbar < 2.66) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{2.66-2.78}{\frac{0.75}{\sqrt{110} } } ) = P(Z < -1.68) = 1 - P(Z  1.68)

                                                              = 1 - 0.95352 = 0.04648

P(Xbar \leq 2.50) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{2.50-2.78}{\frac{0.75}{\sqrt{110} } }  ) = P(Z \leq  -3.92) = 1 - P(Z < 3.92)

                                                              = 1 - 0.99996 = 0.00004  

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

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Answer:

≈ 27 ft

Step-by-step explanation:

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