AChapter 6 TestChapter 6 TestYour disk is almost fullchoices?Save space by optimizing storage.Microsoft AutoUpdateUpdate is ready to be installed.12)12. A restaurant manager estimates that 45% of all customers would order the nightly special if it came with afree dessert. The manager selects a random sample of 50 customers to survey to see if they would order thenightly special if it came with a free dessert.a. Calculate the mean and standard deviation of the sampling distribution of P, the proportion of customersthat answer yes to the survey.b. Justify that the sampling distribution of P is approximately normal.c. Calculate the probability that no more than 40% of the customers sampled answer yes to the survey.13)The scores out of 50 points on a recent vocabulary test for all of the 120 students enrolled in a statistics classat a local high school is approximately normally distributed with a mean of 34.82 points and a standarddeviation of 5.02 noints The teacher plans to select a random samnle of 6 students to survev ahout how to docs.google.comAChapter 6 TestChapter 6 TestYour disk is almost fullSave space by optimizing storage.Microsoft AutoUpdateUpUpdate is ready to be installed.11)Re11. A principal wants to determine if the students like the new healthy choices offered to the students. Thecafeteria manager believes that 70% of the students like the healthy menu options. To test this claim, theprincipal asks 150 randomly selected students and finds that 98 of the students approve of the new healthychoices.a. Identify the population, the parameter, the sample, and the statistic in context. Use correct notation.b. Using the cafeteria manager's claim, the statistics students at the school simulated 50 SRSS from apopulation in which p = 70%. The results of the simulation are shown here.0.7Simulated sample proportion of like the choicesOne of the dots on the graph is p 0.6267. Explain what this dot represents.0.60.650.750.8c. Based on the simulation, is there convincing evidence that the proportion of students that like the healthymenu options at the school is less than the cafeteria manager's claim that 70% of the students like thechoices?

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