A distance is measured six times. The observed values are 572.182 m, 572.140 m, 572.103 m, 572.160 m, 572.125 m, and 572.155 m. All measurements are uncorrelated and their standard deviations are 0.030 m, 0.030 m, 0.030 m, 0.020 m, 0.020 m, and 0.010 m, respectively. Find the least squares estimate for the distance. Use matrices and R in the solution. Write the R commands involved.

A forest ranger has data on the heights of a large growth of young pine trees. The mean height is 3.2 feet and the standard deviation 0.6 feet. A histogram shows that the distribution of heights is approximately normal. Approximately what proportion of the trees should we expect to be between 4.0 and 4.4 feet tall? A) 0.02  B) 0.07   C) 0.91  D) 0.98

Assume the selling prices of homes in a particular community follow a normal distribution with a mean of $263,100 and a standard deviation of $43,200. Complete parts a through c. a. Determine the range of selling prices in this community that includes one standard deviation around the mean. The range is from $ to $ (Type integers or decimals. Use ascending order.) b. Determine the range of selling prices in this community that includes two standard deviations around the mean. The range is from $ to $ (Type integers or decimals. Use ascending order.) c. Determine the range of selling prices in this community that includes three standard deviations around the mean. The range is from $ to $1. (Type integers or decimals. Use ascending order.)

A clinic finds that the average patient stay is 5.7 hours with a standard deviation of 1.8.  If a patient has a relative stay of 2.4, find how many hours the patient was in the clinic. Give a 2-decimal answer