In: Statistics and Probability
1. The time required by a mechanic in a bicycle shop to assemble a certain type of bicycle may be looked upon as a random variable with a mean distribution of 20.5 minutes and a standard deviation of 2.3 minutes. find the probabilities that the time required to assemble a bicycle is:
a. at least 20 minutes
b. at most 19.0 minutes
c. between 2.0 and 21.0 minutes
d. between 18.0 and 20 minutes
a)
µ = 20.5
σ = 2.3
P ( X ≥ 20 ) = P( (X-µ)/σ ≥ (20-20.5) /
2.3)
= P(Z ≥ -0.22 ) = P( Z <
0.217 ) = 0.5860
(answer)
b)
µ = 20.5
σ = 2.3
P( X ≤ 19 ) = P( (X-µ)/σ ≤ (19-20.5)
/2.3)
=P(Z ≤ -0.65 ) =
0.2571 (answer)
c)
µ = 20.5
σ = 2.3
we need to calculate probability for ,
P ( 2 < X <
21 )
=P( (2-20.5)/2.3 < (X-µ)/σ < (21-20.5)/2.3 )
P ( -8.043 < Z <
0.217 )
= P ( Z < 0.217 ) - P ( Z
< -8.04 ) =
0.5860 - 0.0000 =
0.5860 (answer)
d)
we need to calculate probability for ,
P ( 18 < X <
20 )
=P( (18-20.5)/2.3 < (X-µ)/σ < (20-20.5)/2.3 )
P ( -1.087 < Z <
-0.217 )
= P ( Z < -0.217 ) - P ( Z
< -1.09 ) =
0.4140 - 0.1385 =
0.2754 (answer)