aluminium sheets used to make beverage cans have thicknesses that are normally d

Question

aluminium sheets used to make beverage cans have thicknesses that are normally distributed with mean 10 and standard deviation 1.3. a particular sheet is 10.8 thousandths of an inch thick.

1- find z-score of 10.8?

2- the thickness of a certain sheet has a z-score of -1.7, find the thickness of the sheet in the original until of thousandths of inches?

3- find the area under the normal curve to the left of z=0.47?

4- find the area under the normal curve to the right of z=1.38?

5- deduce from the previous question, the area under the normal curve to the left of z=-1.38. then check your answer from the z table.

6- find the area under the normal curve between z=-1.38 and z= 1.38. can we get the answer basing on questions 4 and 5? if yes, how?

7- what z score corresponds to the 75th percentile? find the thickness of the sheet in the original units of thousandths of inches.

8- what z score corresponds to the 25th percentile?

9- can we answer question 8 graphically? if yes, explain.

10- what thickness of the sheet (in the original units of thousandths of inches) corresponds to the median (50th percentile)

please answer the question with details and steps clearlly.

Explanation / Answer

mean 10 sd 1.3 1) z= (x-mean)/sd =(10.8-10)/1.3 0.615384615 2) z = -1.7 = (x-mean)/sd x= = 1.7*1.3+10 x= 12.21 3) p(z1.38) = =1-p(z

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