please show detailed answers... step by step and the slope. If using the compute

Question

please show detailed answers... step by step and the slope.
If using the computer please show how and draw the slope.

Question 3 (25 points) The fill amount of bottles of a soft drink is normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. If a random sample of 25 bottles selected what the probability that the sample mean will be a) Between 1.99 and 2.0 liters? b) Below 1.98 liters? c) Greater than 2.01 liters? that is d) The probability is 90% that the sample mean will contain an amount between which two values (symmetrically distributed around the mean)?

Explanation / Answer

Part-a

Sample mean follows normal distribution with mean =2.0 and standard deviation=0.05/sqrt(25)=0.01

Using excel function =NORMDIST(2,2,0.01,TRUE)-NORMDIST(1.99,2,0.01,TRUE) , we get

P(1.99<xbar<2.0)=0.3413

Part-b

Using excel function =NORMDIST(1.98,2,0.01,TRUE) , we have

P(xbar<1.98)= 0.0228

Part-c

Using excel function =1-NORMDIST(2.01,2,0.01,TRUE) , we have

P(xbar>2.01)= 0.1587

Part-d

We have to find x1 and x2 such that P(x1<xbar<x2)=0.90

By symmetry P(xbar<x1)=0.05 and P(xbar<x2)=0.95

Using excel function =norminv(0.05,2.0,0.01) we get x1=1.98

Using excel function =norminv(0.95,2.0,0.01) we get x2=2.02

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