Question

The fill amount of bottles of a soft drink is normally​ distributed, with a mean of 1.01.0 literliter and a standard deviation of 0.040.04 liter. Suppose you select a random sample of 2525 bottles. a. What is the probability that the sample mean will be between 0.990.99 and 1.01.0 literliter​? b. What is the probability that the sample mean will be below 0.980.98 literliter​? c. What is the probability that the sample mean will be greater than 1.011.01 ​liters? d. The probability is 9999​% that the sample mean amount of soft drink will be at least how​ much? e. The probability is 9999​% that the sample mean amount of soft drink will be between which two values​ (symmetrically distributed around the​ mean)? a. The probability is nothing. ​(Round to three decimal places as​ needed.) b. The probability is nothing. ​(Round to three decimal places as​ needed.) c. The probability is nothing. ​(Round to three decimal places as​ needed.) d. There is a 9999​% probability that the sample mean amount of soft drink will be at least nothing ​liter(s). ​(Round to three decimal places as​ needed.) e. There is a 9999​% probability that the sample mean amount of soft drink will be between nothing ​liter(s) and nothing ​liter(s). ​(Round to three decimal places as needed. Use ascending​ order.)

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Answer 1

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Below is the graphical representation of all parts of the question and short concept before going to solve the questions.

Below is the snapshot of all answer of all parts - Pink coloured cell represents answer.

a part ).

Note that NORM.DIST function is used to calculate the probability. Its notation is given by NORM.DIST(x, mean, std.dev, cumulative). It usually calculate the cumulative probability at given x value.

b part).

C part ).

Follows the same concept as in b part.

d part ).

Note that NORM.INV function has been used to calculate x values corresponding to the probability given. Notation are shown step wise above in d part.

e part).

e).	The probability is 99 ​% that the sample mean amount of soft drink will be between which two values	P (X6 < X < X5) = 0.99	X5 = ?
	As distribution is symmetric therefore we can say that P (X > X5) = 0.005 & P (X < X6) = 0.005
	Therefore for P ( X < X5) = 0.005	X6 = ?	0.979
	Therefore X6 equals to	X6 =	0.979
	Now P (X>X5) is given by 1 - P (X < X5) = 0.995
		P ( X< X5) = 0.995
		X 5 =	1.021

Note : I have used NORM.INV function to evaluate the probabilities as in part d.