Purchase Solution

# Normal and Poisson approsimation to binomial distribution

Not what you're looking for?

A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A.

By using a suitable approximation to the binomial distribution, calculate the probability of A.

The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B.

By using another suitable approximation, calculate probability of B.

Also calculate the probability that B occurs exactly 3 times when 2000 such coins are each tossed 100 times on everyday of a given week.

##### Solution Summary

The solution addresses a fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A.

By using a suitable approximation to the binomial distribution, calculate the probability of A.

The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B.

By using another suitable approximation, calculate probability of B.

Also calculate the probability that B occurs exactly 3 times when 2000 such coins are each tossed 100 times on everyday of a given week.

##### Solution Preview

Let X be the number of heads.
X ~ Bin (100, 0.5)

Since n=100 is large, p= 0.5 is not too small, such that
np = 50 >5 and nq = 50 >5

We use the normal approximation to binomial distribution
X ~N ...

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.