A standard fluorescent tube has a lifelength that is normally distributed with a

Question

A standard fluorescent tube has a lifelength that is normally distributed with a mean of 7000 hours and a standard deviation of 1000 hours. A competitor has developed a compact fluorescent lighting system that will fit into incandescent sockets. It claims that the new compact tube has a lifelength that is normally distributed with a mean of 7500 hours and a standard deviation of 1200 hours.

(a) Which fluorescent tube is more likely to have a lifelength greater than 9000 hours? Why?

(b) Which tube is more likely to have a lifelength of less than 5000 hours? Why?

Explanation / Answer

A. use the normal distribution table

Standard tube: = 7000 and = 1000
9000 hours is 2 above . (i.e., Z = 2)
P(Life > 9,000 hours) = 2.28%

Compact tube: = 7500 and = 1200
9000 hours is 1.25 above (i.e., Z = 1.25)
P(Life > 9,000 hours) = 10.56%

B.

Standard tube: = 7000 and = 1000
5000 hours is 2 below . (i.e., Z = 2)
P(Life < 5,000 hours) = 2.28%

Compact tube: = 7500 and = 1200
5000 hours is 2.083 below (i.e., Z = 2.083)
P(Life < 5,000 hours) = 1.88%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.