The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.3 inch. (a) what is the probability that a randomly selected board cut by the machine has a length greater than 100.12 inches? (b) a sample of 41 boards is randomly selected. what is the probability that their mean length is greater than 100.12 inches?

a) 0.345

b) 0.005

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 0.3

We are given that the distribution of lengths of lumber is a bell shaped distribution that is a normal distribution.

Formula:

a) P(length greater than 100.12 inches)

P(x > 100.12)

Calculation the value from standard normal z table, we have,  

b) Standard error due to sampling:

P(length greater than 100.12 inches for the sample)

P(x > 100.12)

Calculation the value from standard normal z table, we have,  

no

step-by-step explanation:

2-7=-5

7-2=5

when you combing like terms for ech expression, 5 and -5. these numbers are not equal to each other.

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.