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- Describing the sampling distribution of the sample means from an infinite population. The best way to solve this is to use the CENTRAL LIMIT THEOREM.The life of Sunshine CD players is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for 3 years. We are interested in the length of time a CD player lasts. Find the probability that a CD player will break down during the guarantee period. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability. P(0 < x < ____________) = ___________ (Use zero for the minimum value of x.)IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=X= IQ of an individual.(a) Find the z-score for an IQ of 106, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 106. (c) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place). Shade: . Click and drag the arrows to adjust the values. -1.5
- make frequency distribution table where there is the class interval and the frequency. use appropriate solution for class interval. use Sturges formula for number of classes and range over the no. of classes for the class size. this will lead to creating class interval.Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65 15.40 Date Jul 16 Aug 16 Sept 16 Oct 16 Nov 16 Dec 16 Hours light 15.10 13.90 12.30 10.71 9.30 8.60 a. Find the intervals of increase and decrease using test intervals b. Find the intervals of concavity using test interval chartCentral Limit Theorem The average number of liters of fresh milk that a person consumes more than 16 liters per month is 18 liters. Assume that the standard deviation is 4.5 liters and the distribution is approximately normal. a. Find the probability that a person selected at random consumes more than 16 liters per month b. If a sample of 32 individuals is selected, find the probability that the mean of the sample will be more than 16 liters.
- Mid point of class intervals distribution Ause formulaChebyshev’s Rule and the Empirical Rule are rules we use to find intervals where certain amounts of data from a data set is likely to fall. Chebyshev’s Rule can be used for any set of data, and guarantees that At least 3/4 of the data (75 %) falls within 2 standard deviations of the mean. At least 8/9 of the data ( 89 %) falls within 3 standard deviations of the mean. Empirical Rule can be used when data is symmetric and bell-shaped, and predicts that Approximately 95 % of the data falls within 2 standard deviations of the mean. Approximately 99.7 % of the data falls within 3 standard deviations of the mean. Use the above information to answer the following question. Suppose that a set of test scores has sample mean of 67 and sample standard deviation of approximately 6.2. According to Chebyshev’s Rule, at least 75 % of the test scores will fall between Blank 1. Calculate the answer by read surrounding text. and Blank 2. Calculate the answer by read surrounding…True/False Censoring occurs when the event of interest (e.g., disease status) is observed on every individual, usually due to time constraints. The incidence rate (IR), is computed by taking the ratio of the number of new cases of disease to the total number of person-time units available. The prevalence of a disease depends on the incidence of the disease as well as the duration of the disease.
- PROBABILITY DISTRIBUTIONS DISCRETE AND CONTINUOUS A calibration study needs to be conducted to see if the readings on 15 test machines are giving similar results. In how many ways can 5 of the 15 machines be selected for the initial investigation?Poisson approximation of binomial distribution..Applying the Central Limit Theorem: The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. The current amount of somatic cells (common name "pus") allowed in 1 cc of milk is currently set at 750, 000 . Suppose a random sample of 50 1 specimens is gathered and results in a sample mean of 767053 pus cells . 1. Why is the sampling distribution approximately normal? 2. Assuming a population mean of 750.000 cells and a population standard deviation of 85000 cells: what is the mean of the sampling distribution? 3. what is the standard deviation of the sampling distribution? 4. what is the probability that a simple random sample of 50 1 cc specimens has a mean of at least 767053 pus cells? 5. Is this unusual? Use rule of thumb that events with probability less than 5% are considered unusual.