Question
The yield in pounds from a day's production is normally distributed with a mean of 1500 pounds and standard deviation of 100 pounds. Assume that the yields on different days are independent random variables.(a) What is the probability that the production yield exceeds 1400 pounds on each of five days next week?(b) What is the probability that the production yield exceeds 1400 pounds on at least four of the five days next week?
Step 1
The mean of the normal distribution is denoted as $\mu$, such that $\mu = 1500$. The standard deviation is denoted as $\sigma$, such that $\sigma = 100$. Show more…
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6. The yield in pounds from a day's production is normally distributed with a mean of 1500 pounds and a standard deviation of 100 pounds. Assume that the yields on different days are independent random variables. A. What is the probability that the production yield will be greater than 1400 pounds on at most two of five days next week? B. What is the probability that the production yield will be less than 1550 pounds on at least four of the five days next week?
Suppose packages of cream cheese coming from an automated processor have weights that are normally distributed. For one day's production run, the mean is 8.2 ounces and the standard deviation is 0.1 ounce. (a) If the packages of cream cheese are labeled 8 ounces, what proportion of the packages weigh less than the labeled amount? (b) If only $5 \%$ of the packages exceed a specified weight $w$, what is the value of $w$ ? (c) Suppose two packages are selected at random from the day's production. What is the probability that the average weight of the two packages is less than 8.3 ounces? (d) Suppose 5 packages are selected at random from the day's production. What is the probability that at most one package weighs at least 8.3 ounces?
Vibration in Repeated Samples-Sampling Distributions
Review Exercises
The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a. What is the area between 415 pounds and the mean of 400 pounds? b. What is the area between the mean and 395 pounds? c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
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