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Home Question Bank Math Statistics Archive 2024 November 10

Statistics Questions from Nov 10,2024

Browse the Statistics Q&A Archive for Nov 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Suppose a large shipment of compact discs contained \( 14 \% \) defectives. If a sample of size 447 is selected, what is the probability that the sample proportion will be less than \( 10 \% \) ? Round your answer to four decimal places. Suppose \( 49 \% \) of the population has a retirement account. If a random sample of size 896 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than \( 3 \% \) ? Round your answer to four decimal places. Which of the following is a good point estimator for the population standard deviation? The combined SAT scores for the students at a local high school are normally distributed with a mean of 1495 and a standard deviation of 299 . The local college includes a minimum score of 1286 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? \( P(X>1286)=\square \) Enter your answer as a percent accurate to 1 decimal place (do not enter the "\%" sign). Answers obtained using exact \( z \)-scores or \( z \)-scores rounded to 3 decimal places are accepted. Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of \( 0^{\circ} \mathrm{C} \) and a standard deviation of \( 1.00^{\circ} \mathrm{C} \). A single thermometer is randomly selected and tested. Find \( P_{7} \), the 7 - percentile. This is the temperature reading separating the bottom \( 7 \% \) from the top \( 93 \% \). \( P_{7}=\square \) (Round answer to three decimal places) What does it mean to say that two variables are positively associated? A. There is a linear relationship between the variables. B. There is a relationship between the variables that is not linear. C. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. D. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases. What does it mean to say that two variables are negatively associated? A. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable decreases. B. There is a linear relationship between the variables, and whenever the value of one variable increases, the value of the other variable increases. C. There is a relationship between the variables that is not linear. D. There is a linear relationship between the variables. The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.977 g and a standard deviation of 0.325 g . Find the probability of randomly selecting a cigarette with 0.522 g of nicotine or less. \( \mathrm{P}(X<0.522 \mathrm{~g})=\square \) Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact \( z \)-scores or \( z \)-scores rounded to 3 decimal places are accepted. Identify the sampling technique used for the following study. \[ \text { A random number generator is used to choose five metropolitan areas. Then a college student collects data from each person In these metropolitan areas. } \] \[ \text { Answer } \] O Stratified Sampling In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 65 and a standard deviation of 3 . Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 56 and 74 ? Do not enter the percent symbol. ans \( =\square \% \) A statistician calculates that \( 8 \% \) of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 694 Americans would differ from the population proportion by less than \( 3 \% \) ? Round your answer to four decimal places.
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