Approximate the Following Binomial Probabilities by the Use of Normal $\le$

question 38

Essay

Approximate the following binomial probabilities by the use of normal approximation.
a.P(X = 18,n = 50,p = 0.3)
b.P(X $\le$ 15,n = 50,p = 0.3)
c.P(X $\le$ 12,n = 50,p = 0.3)
d.P(12 $\le$ X $\le$ 18,n = 50,p = 0.3)

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Definitions:

Early Renaissance

A period in European art history, roughly the 14th to the early 16th century, marked by a revival of interest in the classical art and philosophy of ancient Greece and Rome.

Madonna of the Rocks

An iconic Renaissance painting by Leonardo da Vinci depicting the Virgin Mary with the infant Jesus, John the Baptist, and an angel in a rocky setting.

Bramante

Donato Bramante, an Italian architect who introduced Renaissance architecture to Milan and the High Renaissance style to Rome, with St. Peter’s Basilica being among his most famed works.

Saint Peter's

A renowned basilica in Vatican City, serving as one of the most significant sites of Catholic worship and pilgrimage, notable for its grand architecture.