Estadísticas preguntas y respuestas

Partie B : VPP et maladie rare On dispose d'un test pour dépister une maladie rare. Le fabricant du test fournit les caractéris- tiques suivantes: - la probabilité qu'un individu malade ait un test positif est de 0,99 ; - la probabilité qu'un individu non malade ait un test négatif est de 0,99 . On envisage un dépistage systématique sur une population dans laquelle on estime à \( f \) (avec \( 0 \leqslant f \leqslant 1 \) ) la proportion de gens malades. 1. Expliquer pourquoi VPP \( =\frac{99 f}{98 f+1} \).

3. ( \( \$ \) points) Major League Baseball requires that its baseballs weigh at least 142 grams and no more than 149 grams. The weights of baseballs manufactured by a particular company are normally distributed with mean 146.5 grams and standard deviation 1.9 grams. What proportion of baseballs made by this company meet the major league standard for weight? (Round your answer to 3 decimal places.)

3. (s points) Major League Baseball requires that its baseballs weigh at least 142 grams and no more than 149 grams. The weights of baseballs manufactured by a particular company are normally distributed with mean 146.5 grams and standard deviation 1.9 grams. What proportion of baseballs made by this company meet the major league standard for weight? (Round your answer to 3 decimal places.)

2. (8 points) Suppose that the weight of a particular brand of cercal in boxes labeled " 18 oz " is normally distributed with mean 18.4 oz and standard deviation 0.26 oz . What is the probability that a randomly selected box will have at least 18 oz of cereal? (Round to 3 decimal places.)

A biologist wants to know the mean weight of fish in a particular lake. She traps a random selection of 18 fish and weighs each of them. She finds that \( \bar{x}-327 \) grams and \( s=31 \) grams. Construct a \( 90 \% \) confidence interval for the mean weight of fish in the lake. Round the boundaries of the interval to one decimal place. The \( 90 \% \) confidence interval is: Submit Question

A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorde The mean weight was \( \mu= \) two grams with a standard deviation of \( \sigma=0.12 \) grams. The opulation standard deviation is known to be \( \sigma=0.1 \) grams. Construct a \( 90 \% \) confidence nterval for the population mean weight of the candies. I. State the confidence interval. II. Sketch the graph. III. Calculate the error bound.

A set of final examination grades in an introductory statistics cours is normally distributed, with a mean of 73 and a standard deviation 8 . (a) What is the probability that a student scored below 91 on this exam (b) What is the probability that a student scored between 65 and 89 ? (c) The probability is \( 5 \% \) that a student taking the test scores higher th what grade? (d) If the professor grades on a curve (i.e., gives A's to the top \( 10 \% \) of class, regardless of the score), are you better off with a grade of 81 this exam or a grade of 68 on a different exam, where the mean is 6 and the standard deviation is 3? Show your answer statistically and explain.

Exercice 3: \( \quad(\quad / 2 \) pts) Un pâtissier a vendu l'an dernier 10000 gâteaux à \( 10 € \) et 100 gâteaux de mariage à \( 1000 € \). Cette année, il vend 10000 gâteaux à \( 8 € \) et 100 gâteaux de mariage à \( 1300 € \). II dit: : "Mes clients sont contents: le prix médian de mes gâteaux a baissé. Mon comptable est content:le prix moyen de mes gâteaux a augmenté.» Que peut-on penser de ces affirmations?

5 The data below shows the number of aces served by a player in each of their grand slam tennis matches for the year. \( 15 \quad 22 \) 11 17 15

5 The data below shows the number of aces served by a player in each of their grand slam tennis matches for the year. \( \begin{array}{lllllllllllllll}15 & 22 & 11 & 17 & 25 & 25 & 12 & 31 & 26 & 18 & 32 & 11 & 25 & 32 & 13 \\ \text { a } & 10\end{array} \) Construct a stem-and-leaf plot for the data. b From the stem-and-leaf plot, find the mode and median number of aces. c is the data symmetrical or skewed?