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,  

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.