Mathematics: How many solutions does the system have?

The answer is 0.274 and 0.841 Step-by-step explanation:Given:In this question, let X the binomial random variable with the parameters: Calculating the random variable Z: is an approximately regular, cumulative random variable with specified in the back of the book in the tables. Using the continuity and tables to calculate:...

How many solutions does the system have? - id1741471, jessicathegr823

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hannahbrown889

17.04.2023

Mathematics

The answer is "0.274 and 0.841"

Step-by-step explanation:

Given:

In this question, let X the binomial random variable with the parameters:

$n = 1000\\\\P = 0.193$

Calculating the random variable Z:

$Z= \frac{X - np}{\sqrt{np(l - p)}}=\frac{x -193}{12.48}$

is an approximately regular, cumulative random variable with $\Phi$ specified in the back of the book in the tables.

Using the continuity and tables to calculate:

$\to \mathbb{P} (X 200) = \mathbb{P} (X\geq 200.5) \approx \mathbb{P}(Z\geq 0.6)=1- \Phi(0.6) \approx 0.274 \\\\\to \mathbb{P} (180 < X < 300) = \mathbb{P} (180.5 \leq X \leq 299.5) = \approx \mathbb{P} (-1 \leq Z\leq 8.53) = \approx 1- \Phi(-1) \approx 0.841$

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