Question

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of six syringes taken from the batch. Suppose the batch contains 1% defective syringes.

(a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, …, 5 and 6 defective syringes in a random sample of six syringes. (Select the correct graph.) A histogram with 4 visible bars is given. The horizontal axis is labeled: r. The vertical axis is labeled: P(r). The leftmost bar is centered on the value 0 and is approximately 0.69 units tall. Moving to the right, the second bar is centered on the value 1 and is approximately 0.26 units tall. The third bar is centered on the value 2 and is approximately 0.04 units tall. The fourth bar is centered on the value 3 is very close to 0 units tall. The values 4, 5, 6, are also labeled on the horizontal axis. There are no visible bars over these labels. A histogram with 6 visible bars is given. The horizontal axis is labeled: r. The vertical axis is labeled: P(r). The leftmost bar is centered on the value 0 and is approximately 0.35 units tall. Moving to the right, the second bar is centered on the value 1 and is approximately 0.40 units tall. The third bar is centered on the value 2 and is approximately 0.19 units tall. The fourth bar is centered on the value 3 and is approximately 0.05 units tall. The fifth bar is centered on the value 4 and is approximately 0.01 units tall. The sixth bar is centered on the value 5 is very close to 0 units tall. The value 6, is also labeled on the horizontal axis. There is no visible bar over this label. A histogram with 5 visible bars is given. The horizontal axis is labeled: r. The vertical axis is labeled: P(r). The leftmost bar is centered on the value 0 and is approximately 0.50 units tall. Moving to the right, the second bar is centered on the value 1 and is approximately 0.37 units tall. The third bar is centered on the value 2 and is approximately 0.11 units tall. The fourth bar is centered on the value 3 and is approximately 0.02 units tall. The fifth bar is centered on the value 4 is very close to 0 units tall. The values 5, 6, are also labeled on the horizontal axis. There are no visible bars over these labels. A histogram with 3 visible bars is given. The horizontal axis is labeled: r. The vertical axis is labeled: P(r). The leftmost bar is centered on the value 0 and is approximately 0.94 units tall. Moving to the right, the second bar is centered on the value 1 and is approximately 0.06 units tall. The third bar is centered on the value 2 is very close to 0 units tall. The values 3, 4, 5, 6, are also labeled on the horizontal axis. There are no visible bars over these labels. Incorrect: Your answer is incorrect.

(b) Find μ (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.) μ = 0.06 Correct: Your answer is correct. syringes What is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.) 0.360 Incorrect: Your answer is incorrect. syringes

(c) What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.) 0.9973 Incorrect: Your answer is incorrect.

(d) Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.) σ = 0.281 Incorrect: Your answer is incorrect. syringes

Answer 1

a)

b)

μ =np=6*0.01 =0.06

e expected number of defective syringes the inspector will find =0.06

c)

probability that the batch will be accepted =P(r<=1) =0.999

d)

σ =sqrt(np(1-p)=sqrt(6*0.01*0.99)=0.244