TKK Products manufactures 50-, 60-, 75-, and 100-watt electric light bulbs. Labo

Question

TKK Products manufactures 50-, 60-, 75-, and 100-watt electric light bulbs. Laboratory tests show that the lives of these light bulbs are normally distributed with a mean of 550 hr and standard deviation of 150 hr, What is the probability that a TKK light bulb selected at random will bum for the following times? (Round your answers to four decimal places) (a) more than 750 hr (b) less than 450 hr (c) between 550 and 750 hr (d) between 450 and 600 hr The distribution of heights of adult males is normally distributed with mean 68 inches and standard deviation 2.9 inches. Answer the following. (Round your answers to 2 decimal places.) (a) What minimum height is taller than 64% of all adult males? inches (b) What 2 heights that are symmetric about the mean enclose the middle 82% of all heights? lower value: inches upper value: inches

Explanation / Answer

Given mean = 68 and SD = 2.9.

(a) What minimum height is taller than 64% of all adult males:

P(Z>X) = 1 - P(Z<X) = 1-0.64 = 0.36. From the normal distribution tables this value coincides with a z value of -0.36

Z = (X - Mean)/SD

Therefore -0.36 = (X - 68)/2.9. Solving we get X = 66.96

(b) Since it is distributed equally about the mean then -X <= Z < X = 2P(X) - 1 = 0.82

Therefore 2 P(X) = 1.82 or P(X) = 1.82/2 = 0.91

The z value corresponding to the value of 0.91 is 1.34

Since Z = (X-Mean)/SD

1.34 = X-68/2.9

Solving X = 71.89. Now, 71.89 is +3.89 above the mean, and therefore

The Lower value = 68-3.89 = 64.11

and The Upper Value = 71.89

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