A machine produces bottle caps. The machine is calibrated to produce bottle caps with a mean diameter of 2.8 cm and standard deviation of 0.03 cm. Let X represent the random variable for diameter of bottle caps. Leave your answers as a percent without rounding.
Question 1
What percent of bottle caps are between 2.77 cm and 2.83 cm?
Question 2
Find P(2.74 ≤ x ≤ 2.86). (Percentage)
Question 3
What percent of bottle caps are less than 2.71 cm?
Question 4
Find P(X ≥ 2.86) (Percentage)
Question 5
What percent of bottle caps are exactly 2.8 cm?

Question 6
If all caps that are smaller than 2.71 cm and greater than 2.89 cm are rejected/thrown out, what percent would be lost?
Men's Shoe Designer
A men's shoe designer is willing to accommodate 95% of the male population. If the mean foot length is 25.25 cm and the standard deviation is 3.875 cm, answer the following:
Question 7
What is the smallest foot length the designed is willing to accommodate?
Question 8
What is the largest foot length the designed is willing to accommodate?