Consider the probability that no fewer than 75 out of 111 houses will lose power

aflacatn

aflacatn

Answered question

2021-09-24

Consider the probability that no fewer than 75 out of 111 houses will lose power once a year. Assume the probability that a given house will lose power once a year is 98%.
Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
A) Yes
B) No

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-09-25Added 95 answers

Step 1
Given:
n=111
Probability of success p=0.98
q=1p=10.98=0.02
Solution:
Normal condition for sampling distribution of sample proportion:
If np10
and nq10
The sampling distribution is normal.
Step 2
np=111×0.98
=108.78
nq=111×0.02
nq=2.22
Since nq is not greater than or equal to 10, so we can not use Normal curve as an approximation to the Binomial probability.
Step 3 Answer: No
nq=2.22
Since nq is not greater than or equal to 10, so we can not use Normal curve as an approximation to the Binomial probability.

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