Use the z-score table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.
A manufacturer of light bulbs finds that one light bulb model has a mean life span of 1027 h with a standard deviation of 90 h.
What percent of these light bulbs will last as follows? (Round your answers to one decimal place.) (a) at least 970 h % (b) between 820 and 880 h
Given:
= 1027, = 90
Let X be the Life span of light bulb
a) at least 970 h %
Find: P(X > 970)
P(X > 970) = P(Z > -0.63)
P(X > 970) = 1 - P(Z < -0.63)
P(X > 970) = 1 - 0.263..............Using standard Normal table
P(X > 970) = 0.737 = 73.7%
At least 73.7% of these light bulbs will last at lest 970 h%
b)
Find: P(820 < X < 880)
P(820 < X < 880) = P(-2.30 < Z < -1.63)
P(820 < X < 880) = P(Z < -1.63) - P(Z < -2.30)
P(820 < X < 880) = 0.0512 - 0.0107 ..............Using standard Normal table
P(820 < X < 880) = 0.040 = 4.0%
At least 4.0% of these light bulbs will last between 820 and 880 h.
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