In a "torture test" a light switch is turned on and off until it fails. if the probability that the switch will fail any time it
1 answer:
The probability that the switch does not fail is 1-0.001=0.999. In order to switch the lights off and on 1200 times, we need to press the switch 2400 times. Each event is assumed independent from the others; when we press the switch, its probability that it will fail is not influenced by the previous pressing of the switch. Thus, the probability that it won't fail after 2 times is 0.999*0.999=0.999^2. Similarly, we get that the required probability is : 
This is a relatively low probability. We see that even if the probability that the switch fails one time is very low, after many repetitions it becomes quite probable that the switch will fail at least one time.
This is a relatively low probability. We see that even if the probability that the switch fails one time is very low, after many repetitions it becomes quite probable that the switch will fail at least one time.
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Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is and the standard deviation is
In this problem, we have that:
.
So
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.