Question

Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ = 6 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round your answers to four decimal places.)

(b) P(x < 6.2)=

(d) P(5.6 < x < 6.2) =  

(e) P(x > 5.5) =  

(f) P(x > 4.8) =

An article reported that what airline passengers like to do most on long flights is rest or sleep; in a survey of 3697 passengers, almost 70% did so. Suppose that for a particular route the actual percentage is exactly 70%, and consider randomly selecting nine passengers. Then x, the number among the selected nine who rested or slept, is a binomial random variable with n = 9 and p = 0.7. (Round your answers to four decimal places.)

(a) Calculate p(6).
p(6) =  

(b) Calculate p(9), the probability that all nine selected passengers rested or slept.
p(9) =  

(c) Determine P(x ≥ 6).
P(x ≥ 6) =

Interpret this probability.

This is the probability that exactly 6 out of 10 selected passengers rested or slept.This is the probability that at least 6 out of 10 selected passengers rested or slept.     This is the probability that exactly 6 out of 9 selected passengers rested or slept.This is the probability that at least 6 out of 9 selected passengers rested or slept.

NBC News reported that 1 in 20 children in the U.S. has a food allergy.† Consider selecting 15 children at random. Define the random variable x as

x = number of children in the sample of 15 that have a food allergy.

Find the following probabilities. (Round your answers to three decimal places.)

(a)

P(x < 2)

(b)

P(x ≤ 2)

(c)

P(x ≥ 3)

(d)

P(1 ≤ x ≤ 2)

Industrial quality control programs often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. A lot might be judged acceptable if one or fewer defective parts are found among those inspected. Otherwise, the lot is rejected and returned to the supplier. Use technology or Appendix Table 9 to find the probability of accepting lots that have each of the following. (Hint: Identify success with a defective part. Round your answers to three decimal places.)

(a)  5% defective parts
P(lot will be accepted) =  

(b)  20% defective parts
P(lot will be accepted) =  

(c)  25% defective parts
P(lot will be accepted) =

Answer 1