Normal Distribution Questions and Answers

The volume of dish washing liquid in a satchet is normally distributed with mean 400 ml and standard deviation 45 ml. The volume of fabric softener in a bottle is normally distributed with mean 650 ml and standard deviation 50 ml, independently of the satchets. Find the probability that the total volume of 4 randomly chosen satchets is less than the total volume of 2 randomly chosen bottles.

A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than 1.95 kg. Find the standard deviation of the packet weights, correct to 3 decimal places (in kg).

A machine packs washing powder into packets that are normally distributed with mean 2 kg and standard deviation 0.039 kg. Find the proportion of packets that weigh more than 2.10 kg.

The volume of dish washing liquid in satchets is normally distributed with mean 400 ml and standard deviation 45 ml, independent of the volume of fabric softener in bottles, which is normally distributed with mean 650 ml and standard deviation 50 ml. Let W be the total volume of 2 randomly chosen bottles of fabric softener minus the total volume of 4 randomly chosen satchets of dish washing liquid. What is the standard deviation of W, in ml (to 1 decimal place)?

A new detergent is made by mixing the contents of 1 satchet of dish washing liquid, mean volume 400 ml, with 2 bottles of fabric softener, mean volume 650 ml per bottle. What is the expected total volume of the new detergent, in ml?

A machine packs washing powder into packets with mean weight 2 kg. The weights are normally distributed, and 10% of packets weigh less than 1,95 kg. What is the standard deviation of the packet weights, in kg (to 3 decimal places)?

Packets of washing powder have weights normally distributed with mean 2 kg and standard deviation 0,039 kg. What proportion of packets weigh more than 2,10 kg? Give your answer to 3 decimal places or as a percentage.

A factory produces two types of nut and bolt with normally distributed masses. Type A bolts have mean mass 20.5 g and Type A nuts have mean mass 5 g; Type B bolts have mean mass 20 g and Type B nuts have mean mass 4.7 g. Each bolt is fitted with two nuts. What is the mean, in grams, of (total mass of a Type A bolt-and-nuts unit) minus (total mass of a Type B bolt-and-nuts unit)?

A factory produces two types of nut and bolt with independent, normally distributed masses, each with standard deviation 0.2 g. Type A bolts have mean 20.5 g and Type A nuts have mean 5 g; Type B bolts have mean 20 g and Type B nuts have mean 4.7 g. Each bolt is fitted with two nuts. What is the probability that the total mass of a Type A bolt-and-nuts unit is greater than the total mass of a Type B bolt-and-nuts unit?

The diameters of washers produced by a machine follow a Normal distribution with standard deviation 0.1 mm and unknown mean $\mu$. The mean is to be set so that the probability that a diameter exceeds 2.0 mm is 0.03.