The lifetimes of lightbulbs produced by a particular manufacturer have an approx
ID: 3332373 • Letter: T
Question
The lifetimes of lightbulbs produced by a particular manufacturer have an approximately normal distribution with a mean of 217 hours and a standard deviation of 24 hours. Suppose that you purchase 9 bulbs, which can be regarded as a random sample from the manufacturer's output. 236,2.4,2.38, 0.0086999999999999 ROUND YOUR ANSWERS TO FOUR DECIMAL PLACES. (a). The sampling distribution of the sample mean lifetime of these 9 bulbs is norm with a mean of 217and a standard error of 24 Using your answer from part (a), find the probability that the sample mean lifetime of these 9 bulbs is (b), less than 196 L (c), greater than 236 (d), between 201 and 239 | |Explanation / Answer
THe four part
(A) THe sampling distribution of the sample mean lifetime of these 9 bulbs is normal with a mean of 217 hours and a standard error of s/ sqrt(n) = 24/ sqrt(9) = 24/ 3 = 8 hours.
(B) Less than 196.
Pr( X <= 196) = NORMAL (X <= 196 ; 217; 8)
Z = (196 - 217)/ 8 = -2.625
Pr( X <= 196) = 0.0043
(C) Pr(X >= 236) = 1 - Pr(X < 236)
NORMAL (X <= 236 ; 217; 8)
Z = (236 - 217)/ 8 = 2.375
Pr( X <= 236) = 0.9912
Pr(X >= 236) = 1 - Pr(X < 236) = 1 - 0.9912 = 0.0088
(c) Pr( 201 <= X <= 239) = Pr( X < = 239 ; 217; 8) - Pr(X <= 201 ; 217 ; 8)
Z - values
Z2 = (239 - 217)/ 8 = 2.75
Z1 = (201 - 217)/8 = -2
Pr( 201 <= X <= 239) = Pr( X < = 239 ; 217; 8) - Pr(X <= 201 ; 217 ; 8) = (2.75) - (-2)
= 0.9970 - 0.0228
= 0.9742
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