Use a normal distribution as an approximation to the binomial

mattgondek4

mattgondek4

Answered question

2021-10-01

Use a normal distribution as an approximation to the binomial probability distribution to approximate the probability of more than 13 successes in 20 tries, if each try has a success probability of p=0.8.

Answer & Explanation

BleabyinfibiaG

BleabyinfibiaG

Skilled2021-10-02Added 118 answers

Step 1
Given:
Sample Size (n)=20
Proportion (p)=0.8
The normal distribution can be used as an approximation to the binomial probability distribution by applying continuity correction.
Step 2
The probability of more than 13 successes in 20 tries is calculated as:
P(X>13)=P(X>13.5)
=1P(X<13.5)
=1P(Xnpnpq<13.5(20×0.8)20×0.8×0.2)
=1P(z<1.39754)
=10.081125
=0.918875
Since the area corresponding to z-value -1.39754 is 0.081125 calculated by excel command NORM.S.DIST(-1.39754,TRUE).
Thus the probability is 0.919.

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