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2 years ago

A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?

1 answer:

OverLord2011 [107]2 years ago

5 0

Let's call the 13¢ stamps a and the 18¢ stamps b: a+b = 42 and therefore a= 42-b (formula 1) 0.13a+0.18b= 6.66 In this formula, substitute the value of a according to formula 1: 0.13(42-b)+0.18b= 6.66 Multiply on the left to get rid of the parenthesis: 5.46-0.13b+0.18b= 6.66 Subtract 5.46 from both sides: -0.13b+0.18b= 1.20 Add on the left: 0.05b= 1.20 Divide both sides by 0.05 b= 24 You have 24 18¢ stamps and: 42-24= 18 13¢ stamps Check: (24 x 0.18) + (18 x 0.13)= 6.66 Correct.

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

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

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

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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)

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= 1 - 0.99996 = 0.00004

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

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