You have been hired as a consultant by the Roi du Poisson Seafood Market to work on problems related to inventory. Your first assignment is to determine the size of their weekly order of pickled crappie balls. Suppose that the store has thousands of customers, but only sells an average of eight jars of pickled crappie balls per week. Assume the store is open the same number of hours every day.

(a) Assuming six jars are in stock at the beginning of the week, what is the probability of not having enough jars to meet demand that week?

(b) What is the probability the first sale will occur in the second half of the week?

(c) Assuming no jars are sold in a particular week, what is the average amount of time until the first sale the following week?

Weights of a healthy 10-week-old domestic kitten are normally distributed with an average weight of μ = 24.5 ounces and a standard deviation of σ = 5.25 ounces.

1. What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces?

2a. What is the probability that a healthy 10-week-old kitten will weigh more than 32 ounces?

2b. If the Wilmington Humane Society has twenty healthy10-week-old kittens, about how many will weigh more than 32 ounces? Round to the nearest whole number.

3. If a 10-week-old kitten’s weight is in the bottom 10% of the distribution of weights, then it is said to be undernourished. At what weight is a 10-week-old kitten considered to be undernourished?

Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 148 subjects with positive test results there are 22 false positive results. Among 157 negative results, there are 4 false negative results. Complete parts (a) through (c)

A. How many subjects were included in the study?

The total number of subjects in the study was _

B. How many subjects did not use marijuana?

A total of _ subjects did not use marijuana.

C. What is the probability that a randomly selected subject did not use marijuana?

The probability that a randomly selected subject did not use marijuana is_

​(Do not round until the final answer. Then round to three decimal places as​ needed.)

Subscribers to a store’s coupon distribution list are each emailed a randomly generated discount code which consists of 4 letters followed by 3 digits (some customers may getthe same code). Most codes are for 25% off online shopping on Cyber Monday, but customers whose codes consist of all different letters and 3 digits in increasing order(e.g. MATH014) get 50% off instead.

What is the probability that a code will consist of all different letters and 3 digits in increasing order?

In a group of 10 subscribers, what is the probability that at least two subscribers will get 50% off?

In a group of 1000 subscribers, what is the expected value and standarddeviation for the number of subscribers who will get 50% off?

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean μ = 859 grams and standard deviation of σ = 15 grams.

b) Find the probability that one jar selected at random contains between 841 and 860 grams. (Give your answer correct to four decimal places.)

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)


(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)


(e) Find the probability that a random sample of 20 jars has a mean weight between 841 and 860 grams. (Give your answer correct to four decimal places.)

[12] In an experiment on human behavior, a psychologist asks four men and four women to enter a room and sit at a rectangular table. This table has three seats on each of the longer sides of the table, and one seat at each end of the table. The seats at the end of the table are considered to be the dominant seats. (A diagram may help you to visualize this).

a. If the people choose their seats randomly, determine the probability distribution for the random variable X, where X represents the number of women occupying the end seats. [4]

b. Determine E(X) and Var(X). [5]

c. In 15 independent repetitions of the experiment involving different people each time, calculate the probability that women occupy both end seats 2 or more times. [3]

According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean of 12.8 and a standard deviation of 3.4.

(a) Find the mean and standard deviation of the sampling distribution of for a random sample of size 107. Mean = 12.8 Standard Deviation = 0.328

(c) Find the mean and standard deviation of the sampling distribution of for a random sample of size 397. Mean = 12.8 Standard Deviation = 0.170

(e) If a sample of size 397 is selected from this population, what is the probability that the sample average will be less than 13.1?

probability = ??

I think I have the right answers, except for (e). I have no idea how to do that, so a little help would be appreciated. Thank you!

Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.6 hours of sleep, with a standard deviation of 1.21 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(a) What is the probability that a visually impaired student gets less than 6.9 hours of sleep? answer: 0.0129

(b) What is the probability that a visually impaired student gets between 6.6 and 10.53 hours of sleep? answer: .7728

(c) Fourty percent of students get less than how many hours of sleep on a typical day? answer:

Wholesale of electronic chips receives products from two factories, factory A provides 60%
Of the goods and Factory B supplies 40% of the goods.
From past experience it is known that 20% of the chips of plant A are defective.
It is also known that 50% of all defective chips are supplied by plant B.

A. What percentage of Factory B's chips are defective?

B. What is the probability that a chip that is found to be in good condition is supplied by plant B?
third

C. One after the other, screws supplied from Factory B are sampled. What is the span and variance of the number of chips
That they will have to check until the first invalid is found?

D. Sample 100 chips at random, what is the probability that at least 36 of them are normal chips
Provided by Factory B?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 28 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 28 weeks and that the population standard deviation is 2.5 weeks. Suppose you would like to select a random sample of 72 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 28.5.
P(X > 28.5) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n=72n=72 is randomly selected with a mean greater than 28.5.
P(M > 28.5) =  (Enter your answers as numbers accurate to 4 decimal places.)