A new experimental process for manufacturing a circuit for quantum computers is

illusiia

illusiia

Answered question

2021-09-23

A new experimental process for manufacturing a circuit for quantum computers is successful 80% of the time. Researchers want to calculate the probability that more than 15 of the next 20 attempts to make the circuit will be successful. Can they use the normal approximation to the binomial? Why or why not?

Answer & Explanation

berggansS

berggansS

Skilled2021-09-24Added 91 answers

Step 1
The binomial probability rule states that the probability of (x) success and (n-x) failures in (n) independent trials of the experiment which has (p) as the probability of success in a single trial is obtained by the formula (beg{array}{c}nxend{array})px(1p)nx.
The mean of the binomial random variable obtained by the formula μ=np, where (n) is the number of trials and (p) is the probability of success.
μ=20×0.80
=16
The standard deviation of the binomial random variable obtained by the formula is σ=np(1p), where (n) is the number of trials and (p) is the probability of success.
σ=16(10.80)
=1.78885
Step 2
P(X>15)=1P(z<xμσ)
=1P(z<15161.78885)
=1P(z<0.56)
=10.2877
=0.7123
yes we can use the normal approximation to the binomial.

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