Question

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

Answer 1

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