central limit theorem practice problems
The number of days a student attends classes follows a normal distribution with mean 268 days and a standard deviation of 11 days. 70 students are taken as a sample from the population. What is the statistic’s Expected value and Standard deviation.
The expected value E(x)= 268
The statistic standard deviation will be given by
Customers standing in the queue are served by bank tellers one by one. Given that the expected service time is 2 minutes and the variance is 1. Assume that the service times for the different bank customers are independent. Find the probability that P(90<Y<110) by letting Y be the total time the bank teller spends serving 50 customers
Using the concept of Z-calculations We can write;
Following the requirements of CLT, we know that is tentatively standard normal.
Therefore, the equation will be rewritten as follows;
In a toy production company, the company can produce 1000 toys which would have defects occuring with a probability of 0.1. It is presumed that the defects occurs independently. Find the probability that there are more than 120 defects in a given set of 1000 toys.
The distribution defined above follows a bernoullis distribution
Click Here to see the calculation of Bernoulli Mean
Thus the mean will be p=0.1
The variance of Bernoulli distribution is derived as Click Here
Thus Variance= p(1-p)
Using the CLT we have;
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