Question

Suppose a brand of light bulbs is normalty distributed with a mean ife of 1800 hr and a standard deviation of 150 hr Areas Under the Standard Nomal Curve Find the probability that a light bulb r that brand lasts between 15e0 hr and 1980 hr 1.50 4452 4554 1.30 4002 1.80 1.93 | The protablity thar a ight bulb wllast between 1560 hr and 1980 his□ Type an integer ar decimal ounded 1o four decimal places as needed.)

Answer 1

Let the random vari able X is a brand of light bulbs is normally distributed The mean life is μ= 1800hr The standard deviation is σ=150kr The probability that a light bulb of that brand lasts between 1560 hr and 1960 hr is X<1960)-P( 1560-1800 X-μ 1960-1800 P (1560 < 150 -240 X- u 160 150 P|-1.6 <- <1.066666667 P(-1.6 <z <1.067) σ 150 Since, on using excel functi on normsdist (z) P(z < 1.067)-P(z <-1.6) 0.8569-0.0548 0.8021 P(1560 < X < 1960)~08021 Therefore, the probability that a light bulb of that brand lasts between 1560 hr and 1960 hr is P1560 <X < 1960)~ 0.80211