c) A company claims that the mean amount of alcohol in the sanitizer that they produce is less than \( 35 \mathrm{mg} \) A researcher took a sample of 50 sanitizers and found that the mean is \( 39 \mathrm{mg} \). It is known that the amount of alcohol for all sanitizer is normally distributed with a standard deviation of 14mg. 'population. d) A dietitian in a hospital claims that the mean level of cholesterol for a woman is 169 milligrams per deciliter. Based on the sample of 60 patients, it is found that the mean level of cholesterol is 181 milligrams per deciliter. Assume that the population of level of cholesterol are normally distributed with a standard deviation of 47.2. e) A random sample of 35 bulbs was selected and the specified brightness was evaluated for each bulb by measuring the amount of electric current required. It is found that mean of the current required is 280.3 micro amps and the standard deviation is 10.3 micro amps. It is known that a bulb will burn out if the electric current supplied is more than 290.0 micro amps.