Answer:
The answers to the questions are;
(a) P(At least 1 defective)
= 0.9883.
(b) P(At least 1 defective)
= 0.6409.
Step-by-step explanation:
There are 110 cards and 20 defectives.
a) The probability of at least one defective is given by
P(At least 1 defective) = 1 - P(0 defective)
P(0 defective) = 20C0 × (90C0)/(110C20) = 0.0116
1 - 0.0116 = 0.9883
b) For a set of 110 boards that has 5 defective and 105 non-defective
P(At least 1 defective) = 1 - P(0 defective)
P(0 defective) = (20C0)(90C5)/(110C5) = 0.35909
1-0.35909
= 0.6409
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
The Central Limit Theorem established 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.
In this problem, we have that:
The sample of 112 residents has a mean GPA of 1.7.
By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.
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