A mechanical press is used to mold shapes for plastic toys. When the machine is

Question

A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it produces about 6% defective toys. The toys are manufactured in lots of 250.

A. Check the three conditions to determine if the normal model may be used to approximate the sampling distribution of the sample proportions.

B. A lot is randomly selected, find the probability that at least 9% of the toys are defective.

C. Find the probability that between 7% and 8% of the toys are defective

D. Find the probability that less that 5% of the toys are defective.

Explanation / Answer

Result:

A mechanical press is used to mold shapes for plastic toys. When the machine is adjusted and working well, it produces about 6% defective toys. The toys are manufactured in lots of 250.

A. Check the three conditions to determine if the normal model may be used to approximate the sampling distribution of the sample proportions.

P is fixed and 0.06.

p=0.06, q= 0.94 n=250

np =0.06*250 =15, nq=250*0.94 =235

both np and nq are > 10.

Appropriate to model normal.

B. A lot is randomly selected, find the probability that at least 9% of the toys are defective.

Expectation = np = 15

Variance = np(1 - p) = 14.1

Standard deviation = 3.7550

With continuity correction, z value for 8.5, z=(8.5-15)/3.755 = -1.73

P( x 9) = P( z >-1.73) =0.9582

C. Find th e probability that between 7% and 8% of the toys are defective

z value for 7, z =(7-15)/3.755 = -2.13

z value for 8, z =(8-15)/3.755 = -1.86

P(7<x<8) = P( -2.13<z<-1.86) = P( z< -1.86) – P( z < -2.13)

=0.0314 -0.0166

=0.0148

D. Find the probability that less that 5% of the toys are defective.

With continuity correction, z value for 4.5, z = (4.5-15)/3.755 = -2.80

P( x <5) = P( z < -2.80)

=0.0026

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.