A family built a house and wanted to put down in their rectangular yard. The sod costs $0.32 per square foot plus 10 per square yard to lay the sod. The front yard is 30 by 50 feet. How much will it cost to purchase and lay the sod?

The total cost of purchasing and laying sods in the rectangular yard is $2,146.67  

Step-by-step explanation:

We are given the following in the question:

Dimensions of rectangular yard:

Length = 50 feet

Width = 30 feet

Area of rectangular yard =

Cost of sod = $0.32 per square foot

Total cost of sod =

Cost of laying sods = $10 per square yard

Total cost of laying sod =

Total cost of purchasing and laying the sod =

Thus, the total cost of purchasing and laying sods in the rectangular yard is $2,146.67

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step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.