Activity1 "Rolling a Dice" In rolling an unbiased die, what is the average number of spots that would appear? To answer the given queries, let us follow the following steps: Step 2: Determine the Step 3: Multiply each value probability of each possible outcome Probability P(X) Step 1: Identify all possible outcomes time and its respective probability Number of Spots (X) X.P(X) 1 6. 2 6. 3. 4. 6. EX P(X) = = 3.5 Step 4: Find the sum of the products. Step 5: Interpret the result. The value obtained is called the mean of the random variable X or the mean of the probability distribution of X. The mean tells us that the average number of spots that would appear when an unbiased die is rolled is 3.5. This is correct interpretation even though it is impossible to roll a 3.5 on a 6-sided die. This sort of thing often occurs with expected values. There are five (5) steps to be followed in computing the mean of the probability distribution. Step 1: Identify all possible outcomes. Step 2: Determine the probability of each possible outcome. Step 3: Multiply each value and its respective probabilities. Step 4: Find the sum of their products. Step 5: Interpret the result. 11611611161161 6116

Activity1 "Rolling a Dice" In rolling an unbiased die, what is the average number of spots that would appear? To answer the given queries, let us follow the following steps: Step 2: Determine the Step 3: Multiply each value probability of each possible outcome Probability P(X) Step 1: Identify all possible outcomes time and its respective probability Number of Spots (X) X.P(X) 1 6. 2 6. 3. 4. 6. EX P(X) = = 3.5 Step 4: Find the sum of the products. Step 5: Interpret the result. The value obtained is called the mean of the random variable X or the mean of the probability distribution of X. The mean tells us that the average number of spots that would appear when an unbiased die is rolled is 3.5. This is correct interpretation even though it is impossible to roll a 3.5 on a 6-sided die. This sort of thing often occurs with expected values. There are five (5) steps to be followed in computing the mean of the probability distribution. Step 1: Identify all possible outcomes. Step 2: Determine the probability of each possible outcome. Step 3: Multiply each value and its respective probabilities. Step 4: Find the sum of their products. Step 5: Interpret the result. 11611611161161 6116

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 5E: Population Genetics In the study of population genetics, an important measure of inbreeding is the...

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Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?
The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.025 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 55 43 62 52 69 Copy Data Step 3 of 4 : Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to three decimal places.
The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.0250.025 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 4141 6868 6464 5757 6969 Copy Data Step 1 of 4: State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary. H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ Step 2 of 4: Calculate the expected value for the number of swimmers on Tuesday. Enter your answer as a fraction or a decimal rounded to three decimal places. Step 3 of 4: Compute the value of the…
The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.10 level of significance. Swimmers at the City PoolMonday   Tuesday   Wednesday   Thursday   FridayNumber   46   68   43   51   70 Step 1 of 4 :   State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary. H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯Ha: There is a difference in the number of swimmers from day to day.
The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of ten syringes taken from the batch. Suppose the batch contains 5% defective syringes. (a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, …, 9 and 10 defective syringes in a random sample of ten syringes. (Select the correct graph.)      (b)Find μ (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.) μ = ______ syringes (blank) What is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.) ______syringes (blank) (c) What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.) (d) Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.) σ = ______ syringes (blank)
The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of twelve syringes taken from the batch. Suppose the batch contains 1% defective syringes. (a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, …, 11 and 12 defective syringes in a random sample of twelve syringes. (Select the correct graph.)      (b) Find μ (in terms of the number of syringes). (Enter a number. Enter your answer to two decimal places.)μ =  syringesWhat is the expected number of defective syringes the inspector will find? (Enter a number. Enter your answer to two decimal places.) syringes (c) What is the probability that the batch will be accepted? (Enter a number. Round your answer to three decimal places.) (d) Find σ (in terms of the number of syringes). (Enter a number. Round your answer to three decimal places.)σ =  syringes
A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?
(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 95% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit % upper limit %
The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.01 level of significance. Swimmers at the City Pool Monday Tuesday Wednesday Thursday Friday Number 64 46 41 56 70 Copy Data Step 1 of 4 : State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary. H0H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯HaHa: There is a difference in the number of swimmers from day to day.