A machine at Katz Steel Corporation makes 3-inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean of 3 inches and a standard deviation of 0.10 inch. The quality control inspector takes a sample of 16 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than 2.95 inches or greater than 3.05 inches, the inspector concludes that the machine needs an adjustment. What is the probability that based on a sample of 16 nails, the inspector will conclude that the machine needs an adjustment? Round your answer to 4 decimal places.

The chart below shows the distribution of weeds in yard

Pls! does anybody know a shortcut for answering these types of questions in the future?

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.