Central limit theorem
The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. What is the standard error of the sampling distribution?
20 students are selected at random from a clinical psychology class, find the probability that their mean GPA is more than 5. If the average GPA scored by the entire batch is 4.91. The standard deviation is 0.72.?
The record of weights of the female population follows a normal distribution. Its mean and standard deviation are 65 kg and 14 kg, respectively. If a researcher considers the records of 50 females, then what would be the standard deviation of the chosen sample?
The average weight of a water bottle is 30 kg with a standard deviation of 1.5 kg. If a sample of 45 water bottles is selected at random from a consignment and their weights are measured, find the probability that the mean weight of the sample is less than 28 kg?
The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 90 and 100 months?