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svlad2 [7]
3 years ago
11

hilton university drama club sold 311 tickets for a play. student tickets cost 50 cents each,nonstudent tickets cost $1.50. if t

otal receipts were 385.50, find how many tickets of each type were sold
Mathematics
1 answer:
tamaranim1 [39]3 years ago
4 0

X= number of student tickets

Y= number of on student tickets

x+y=311

0.50x + 1.50y = 385.50


Solve x in 1st equation


X+y=311


X= -y + 311


Now substitute x into second equation to solve for y


0.50(-y+311)+ 1.50y = 385.50


-0.50y+311.50+1.50y=385.50

Y+311.50=385.50


Y= 385.50-311.50


Y= 74


Now substitute y answer to first equation to find x


X+y=311


X+ 74=311


X= 311-74


X= 237


So 237 students tickets and 74 non students tickets



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Using the normal distribution, it is found that:

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c) 0.6811 = 68.11% probability that x is between 60 and 110.

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In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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In this problem:

  • The mean is of 87, thus \mu = 87.
  • The standard deviation is of 25, thus \sigma = 25.

Item a:

This probability is <u>1 subtracted by the p-value of Z when X = 60</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{60 - 87}{25}

Z = -1.08

Z = -1.08 has a p-value of 0.1401.

1 - 0.1401 = 0.8599

0.8599 = 85.99% probability that x is more than 60.

Item b:

This probability is the <u>p-value of Z when X = 110</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{110 - 87}{25}

Z = 0.92

Z = 0.92 has a p-value of 0.8212.

1 - 0.8212 = 0.1788.

0.1788 = 17.88% probability that x is less than 110.

Item c:

This probability is the <u>p-value of Z when X = 110 subtracted by the p-value of Z when X = 60</u>.

From the previous two items, 0.8212 - 0.1401 = 0.6811.

0.6811 = 68.11% probability that x is between 60 and 110.

Item d:

This probability is <u>1 subtracted by the p-value of Z when X = 125</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{125 - 87}{25}

Z = 1.52

Z = 1.52 has a p-value of 0.9357.

1 - 0.9357 = 0.0643.

0.0643 = 6.43% probability that x is greater than 125.

A similar problem is given at brainly.com/question/24863330

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