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3 years ago

Sara is 6 years older than max in 3 years she’ll be 1 1/2 of max’s age . how old is max ?

Mathematics

1 answer:

Andrews [41]3 years ago

4 0

S = m+6
(s + 3) = (m + 3)1.5
When solved m=9 and s=15
When plugged in it works.
So max is 9 years old

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The probability is $P(14 < X < 20 ) = 0.5354$

Step-by-step explanation:

From the question we are told that

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Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

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$X \ \~ \ B( \mu , \sigma )$

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Generally the proportion that are not staying with parents is

$\r q = 1 - \r p$

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The standard deviation is mathematically evaluated as

$\sigma = \sqrt{n * \r p * \r q }$

$\sigma = \sqrt{ 125 * 0.142 * 0.858 }$

$\sigma = 3.90$

Given the n is large then we can use normal approximation to evaluate the probability as follows

$P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90}$

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$P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )$

Generally

$\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )$

$P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )$

$P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )$

$P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)$

So for the z - table

$P( Z< 0.449 ) = 0.67328$

$P(Z < -1.0897) = 0.13792$

$P(14 < X < 20 ) = 0.67328 - 0.13792$

$P(14 < X < 20 ) = 0.5354$

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Answer:

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