Employees of a large corporation are concerned about the declining quality of medical services provided by their group health insurance. A random sample of 100 office visits by employees of this corporation to primary care physicians during the year 2017 found that the doctors spent an average of 19 minutes with each patient. This year a random sample of 108 such visits showed that doctors spent an average of 15.5 minutes with each patient. Assume that the standard deviations for the two populations are 2.7 and 2.1 minutes, respectively. Using the 2.5% level of significance, can you conclude that the mean time spent by doctors with each patient is lower for this year than for 2017? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.
Let X be a continuous random variable with density function "f(x) = \\begin{cases}\n \\frac{x}{2} &\\text{for } 0 \\le x \\le 2 \\\\\n 0 &\\text{, } otherwise\n\\end{cases}"
Find E[|X-E[X]|].
For the following probability distribution:
π(π₯) = ππ|π₯|
, β β β€ π₯ β€ β
Show that π =
1
2
, π
β²
1 = 0, π = β2 and mean deviation about mean is 1.
A machine fills boxes with chocolate balls. The weights of the empty boxes are normally distributed with a mean of 150 g and a standard deviation of 10 g. The mean weight of each chocolate ball is 40 g with a standard deviation of 0.8 g. A full box contains 25 chocolate balls.
a. Calculate the mean weight of a full box of chocolate balls
b. Calculate the standard deviation of the weight of a full box of chocolate balls.
c. Calculate the probability that a full box of chocolate balls weighs less than 1140 g.
d. The company also produces boxes of chocolate squares. It was found that 19% of the boxes
weigh less than 800 g and 28% weigh more than 1200 g. Calculate the mean and standard
deviation of the weight of these boxes
1. There are three brands, say X, Y and Z of an item available in the market. A consumer chooses exactly one of them for his use. He never buys two or more brands simultaneously. The probabilities that he buys brands X, Y and Z are 0.20, 0.16 and 0.45, respectively.
a) What is the probability that he does not buy any of the brands?
b) Given that a customer buys some brand, what is the probability that he buys brand
1. There are three brands, say X, Y and Z of an item available in the market. A consumer chooses exactly one of them for his use. He never buys two or more brands simultaneously. The probabilities that he buys brands X, Y and Z are 0.20, 0.16 and 0.45, respectively.
a) What is the probability that he does not buy any of the brands?
b) Given that a customer buys some brand, what is the probability that he buys brand
Suppose a test for diagnosing COVID-19 is successful in detecting the disease 95% of all persons infected , but itβs incorrectly diagnosing 4% of all health people as having COVID-19 . Suppose also that itβs incorrectly diagnose 12%of all people having another minor disease as having COVID-19 . Itβs known that 2% of the population have COVID-19 , 90% of the population are healthy and 8% have minor diseases.A person selected randomly
Exercise 2.3 Sales personnel for X Company are required to submit weekly reports
listing customer contacts made during the week. A sample of 61 weekly contact
reports showed a mean of 22.4 customer contacts per week for the sales personnel.
A couple has three children.
i. Draw a tree diagram and find the sample space for this experiment.
ii. Find the probability of getting at least one child of each gender.Β
If the likelihood of binominal distribution for a tagged order form is successful probability
is 0.1, what is the probability that there are three tagged order forms in the sample of four?
Required
a. Determining Given n = 4 and p = 0.1 P(X = 3)