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2 years ago

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In a high school there are 1200 students. Estimate the probability that more than 130 students were born in January under each o

f the following assumptions. You do not have to use the continuity correction.
(a) Months are equally likely to contain birthdays
(b) Days are equally likely to be birthdays

1 answer:

ziro4ka [17]2 years ago

3 0

Answer:

The probability that more than 130 students were born in January under the given assumptions is 0.00086

Step-by-step explanation:

Let X be a variable denoting the number of birthdays in January.

P(that a gien birthday is in the month of January) = $\frac{1}{12}$

E(X) = np = $1200\times\frac{1}{12}$ = 100

σ = $\sqrt{ (np ( 1 -p ))}$ = 9.5743

Now, as per question

P (X> 130) = 1 - P( x ≤ 130)

= 1 - P (Z ≤ $\frac{130 - 100}{9.53742}$ )

= 1 - 0.99914

=0.00086

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To find the inverse on this interval, we interchange $x$ and $y$ .

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