An average LCD Projector bulb manufactured by the ABC Corporation lasts 300 days

Question

An average LCD Projector bulb manufactured by the ABC Corporation lasts 300 days with variance of 2500days, By assuming that the bulb life is normally distributed, what is the probability that the bulb will last (i) at most 365 days? (ii) between 250 days and 350 days? The times taken to complete a statistics test by all students are normally distributed with a mean of 55 minutes and a standard deviation of 9 minutes. Find the probability that the mean time taken to complete this test by a class of 36 students would be between 50 and 58 minutes.

Explanation / Answer

Q4)

a) P(X<365)

= P(Z<(365-300)/50

= P(Z<1.3)

= 0.9032

(ii) P(250<X<350)

= P((250-300)/50<Z<(350-300)/50)

= P(-1<z<1)

= 0.6827

Q5) P(50<X<58)

= P((50-55)9)*Sqrt(36)<Z<((58-55)/9)*Sqrt(9))

= 0.9768

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