The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution μ = 0.5 and σ = 0.289. (a) Let x be the sample mean waiting time for a random sample of 12 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.)

The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.

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 the population, we have that:

Mean = 0.5

Standard deviaiton = 0.289

Sample of 12

By the Central Limit Theorem

Mean = 0.5

Standard deviation

The mean of the sampling distribution of x is 0.5 and the standard deviation is 0.083.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.