Question

17) Kevin works at a bike shop. One of his tasks is to assemble bikes. The time it takes him to fully assemble a bike is a normally distributed random variable with My = 21.3 minutes and Oy = 3.0972 minutes. Let Y = the time it takes Kevin to assemble a randomly selected bike. a) Sketch the normal curve for Y. Label the axis below the peak and at the visible edges of the normal curve. b) Shade the area under the normal curve that corresponds to P(Y <15 or Y > 25). c) Use your graph and/or the Empirical Rule to estimate P(Y < 15 or Y > 25).

Answer 1

Part a) Sketch

The red colored area is (mean +- standard deviation)

Normal Distribution: Pr(18.2028<X<24.3972)=0.6827 0.14 0.12 0.10 1 0.08 0.06 1 0.04 0.02 0.00 0 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 N

Given that Yn Nl My , og 2) My 21.3 by = 3.0972 Y = the time it takes Kevin to assemble selected ties bike. randainly Sketch of nound curve for Y. ~Y~Nelly, 642) 0.12 0.10 0.087 0.06 0-04 - 0-02- 4 12 16 20 24 29 32 34 My ay = 18-2028 15213 Mytoy = 24.3972 and P[Y<15 or y>25] PL Yc15] + P[y>25) 15-21.37 3.0972 3.0972 25-21.3 + Pr 7.2113 PE 3.0972 3.0972 P[2c-210341] + P[2 > 1. 1946] 0.021 + 0.1161 11 0.1371

Graphs for part b) & c)

In terms of variable Y:

Area (probability) = 0.1371 12.008 15.106 18.203 21.3 24.397 27.494

In terms of Variable Z:

Area (probability) = 0.1371 -3 -2 -1 0 1 2 3