Question

Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 550 days and a standard deviation of 100 days. The research department randomly selects 25 customers who bought these vacuum cleaners and records the duration (in days) of trouble-free operation. Which of the following is NOT TRUE for the sample average of number of trouble-free operation days ()?  

		P (x̄ < 500) = P(Z < -2.5)
		P (x̄ > 600) = P(Z > 2.5)
		P (x̄ < 520) = P(Z < - 1.5)
		P (550 < x̄ < 580) = 0.9332

Answer 1

Answer:

We have:

Z value:

Option 1: With mean = 500, Z = - 2.5. Correct.

Option 2: With mean = 600, Z = 2.5. Correct.

Option 3: With mean = 520, Z = - 1.5. Correct.

Option 4: With means of 550 and 580, Z range is 0 < Z < 1.5 which implies probability less than 0.9332. Incorrect.

Ans: P (550 < x̄ < 580) = 0.9332 is NOT TRUE.

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