3) El estudio de un cuestionario sobre el grado de satisfacción de los usuarios de servicios públicos revela que la satisfacción sigue una distribución normal, con una nota media de 5,7 puntos y con una desviación típica de 0,5 puntos. a) ¿Cuál es la probabilidad de que la calificación de un usuario esté entre 6 y 7 puntos? (1.25p) b) De 1000 usuarios, ¿cuántos habrán otorgado una nota entre 4 y 6 puntos? (1.75p)

Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.5 hours with a standard deviation of 0.3 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 4.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.

Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.6 hours with a standard deviation of 0.2 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.5 hours to paint each room with a standard deviation of 0.3 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2 . Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.

Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool. Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.5 hours with a standard deviation of 0.3 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 4.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2 . Step 1 of 3 : state the null and alternative hypotheses for the test. Fill in the blank below. \( H_{0}: \mu_{1}=\mu_{2} \) \( H_{a}: \mu_{1} \)

A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 11 bottles of regular cola has a mean of 501.6 mL of soda with a standard deviation of 3.9 mL . A random sample of 14 bottles of diet cola has a mean of 498.9 mL of soda with a standard deviation of 4.5 mL . Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)

Al centro de la curva de distribución normal encontramos el eje de simetría que corresponde a: Desviación estándar Valor tipificado Media aritmética Desviación media