A certain type of batteries is claimed to last on average 19.8 hours of continuo

Question

A certain type of batteries is claimed to last on average 19.8 hours of continuous use. Lives of these batteries are known to be Normally distributed. Answer the following questions.

a. A random sample of 26 batteries was selected and tested, and their standard deviation was found to be 1.73 hours of continuous use. Find is the probability that the average life of these batteries is at least 20.5 hours of continuous use. ANSWER: ___________________________________________________

b. A random sample of 41 batteries was selected and tested, and their standard deviation was found to be 3.17 hours of continuous use. Find the probability that the average life of these batteries is at most 21 hours of continuous use. ANSWER: ___________________________________________________

Explanation / Answer

Solution:- given mean = 19.8

a. standard deviation = 1.73

P(x 20.5) = P(Z (20.5 - 19.8)/1.73)

= P(Z 0.4046)

= 0.3446

b. standard deviation = 3.17

P(x 21) = P(Z (21 - 19.8)/3.17)

= P(Z 0.3785)

= 0.6480

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