Question

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 2.0 liters and a standard deviation of 0.08 liter. Suppose you select a random sample of 25 bottles. a. What is the probability that the sample mean will be between 1.99 and 2.0 liters​? b. What is the probability that the sample mean will be below 1.98 liters​? c. What is the probability that the sample mean will be greater than 2.01 ​liters? d. The probability is 95​% that the sample mean amount of soft drink will be at least how​ much? e. The probability is 95​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)?

Answer 1

Here it is given that distribution is normal with mean=2 and standard deviation=0.08

As population is normal as per central limit theorem distribution of sample mean is also normal

a. Here we need to find

As sample mean is normal, we can convert sample mean to z

b. Here we need to find

3.

d. Here we need to find such that

Using z table we get

So

So

e. Here we need to find such that

Using z table we get  

So

and