2. The maximum allowable limit for mercury in tun

2. The maximum allowable limit for mercury in tuna sushi sold in restaurants is 1ppm. It is known that the amount of mercury found in tuna sushi follows a normal distribution with mean of 0.5ppm and standard deviation 0.2ppm.

(a) What is the probability that a randomly chosen restaurant will have tuna sushi with mercury levels below the allowable limit?

(b) What percentage of restaurants have tuna sushi with mercury levels in the range 0.4ppm to 0.6ppm?

(c) Find the probability that the mean mercury level of tuna sushi from a sample of 13 restaurants will be below 0.65ppm. (d) Calculate the probability that the mean mercury level of tuna sushi from a sample of 13 restaurants is in the range 0.4ppm to 0.6ppm.