1 1 point A random variable x is normally distributed with a mean of 117 and a standard deviation of 14. What is the probability of selecting any random variable from the distribution with a value less than 112? Provide your answer as a percentage to two decimal places. type your answer... 2 1 point A random variable x is normally distributed with a mean of 117 and a standard deviation of 14. P(X s 124)? Provide your answer as a percentage to two decimal places. type your answer... 3 1 point A random variable x is normally distributed with a mean of 117 and a standard deviation of 14. P(X 2 145 )? Provide your answer as a percentage to two decimal places. type your answer...3 points Q The SAT Math scores from 2019 are normally distributed with a mean of 528 and a standard deviation of 117. What is the probability of randomly selecting a test score that is a) less than 495 type your answer... 1 b) between 515 and 690 type your answer... c) greater than 670 type your answer... Provide probabilities rounded to the third decimal place or percentage rounded to the rst decimal place. Source: The College Board 3 points 9 The SAT scores from 2019 are normally distributed with a mean of 1059 and a standard deviation of 210. What is percentage of scores are a) greater than 1200 type your answer... ' b) between 1000 and 1100 type your answer... c) less than 800 type your answer... ' Express all answers as percentage to two decimal places. Source: The College Board a 1 point 9 If the mean of a normal distribution is 45 and the standard deviation is 4.3, how many standard deviations away from the mean is the value 36.8? Write your z-score as a negative or positive number with two decimal places. type your answer... 2 points Calculate the standard error for each of the following problems. Round all answers to four decimal places: a) u = 23.7; o = 4.5; n = 30 type your answer... b) u = 1272.5; 0 = 145.2; n = 100 J type your answer... c) u = 845.9; 0 = 46.8; n = 60 type your answer... J d) u = .024; o = .003; n = 45 J type your answer... J 4 points Calculate the probabilities for each of the following problems. Round all answers to four decimal places: a) For a distribution with u = 23.7; o = 4.5; n = 30, what is the probability of randomly selecting a value less than 22? J type your answer... J b) For a distribution with p = 1272.5; 0 = 145.2; n = 100, what is the probability of randomly selecting a value more than 1290? J type your answer... J c) For a distribution with u = 845.9; a = 46.8; n = 60, what is the probability of randomly selecting a value less than 835? type your answer... d) For a distribution with p = .024; o = .003; n = 45, what is the probability of randomly selecting a value more than .025? J type your answer... J In Question 2, which of those events are signicant? b) d) C) a) 1 point In order to satisfy the Central Limit Theorem, what conditions must be met? Select all that apply. GOOD The population must have a normal distribution The sample size (n) must be at least 30 The sample size (n) must be greater than 1 The population may have any distribution shape, but the sample population must be normal The sample size (n) must represent 5% or more of the population DODCJCJCJ It does not matter what shape the population distribution has because the sampling distribution of the sample means will be normally distributed 1 point For sampling distributions of a sample statistic, select all of the following statements which are true: The mean of the sampling distribution is the mean of the population divided by the sample size (n) The standard deviation of the sampling distribution is the same as the population standard deviation The standard deviation of the sampling distribution can be found by diving the population variance by the sample size (n) and then taking the square root of that value The standard deviation of the sampling distribution is the standard deviation of the population divided by the sample size (n) We do not use the standard deviation of the population, instead we use the standard error The mean of the sampling distribution is the same as the mean of the population CJCJDCJDDD The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size (n) 1 point For sampling distributions of a sample statistic, select all of the following statements which are true: The mean of the sampling distribution is the mean ofthe population divided by the sample size (n) The standard deviation of the sampling distribution is the same as the population standard deviation The standard deviation of the sampling distribution can be found by diving the population variance by the sample size (n) and then taking the square root of that value The standard deviation of the sampling distribution is the standard deviation of the population divided by the sample size (n) We do not use the standard deviation of the population, instead we use the standard error The mean of the sampling distribution is the same as the mean of the population CJCJCJCJCJOD The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size (n) Increasing the sample size (n), has the following effect on the sampling distribution: The greater the sample size (n), the smaller the standard error of the sampling distribution The greater the sample size (n), the smaller the standard deviation of the sampling distribution The greater the sample size (n), smaller the data spread of the sampling distribution OBOE] The greater the sample size (n), the closer the average of the sample statistic will be to the population parameter 2 points Find the z-score associated with the following percentiles to two decimal places a) P12 b) P78 C) P99 type your answer... ' c) P99 = [ type your answer... d)P02 = type your answer... 3) P12 = ' type your answer... ' b) P78 = 2 points Find the z-score to the nearest two decimal places that: a) has 15% of the distribution's area to the right type your answer... ' b) has 22.4% of the distribution's area to the left ' type your answer... ' c) has 99.85% of the distribution's area to the right I type your answer... d) has .15% of the distribution's area to the left type your answer... 4 points Between what two z-scores, to the nearest three decimal places, would we nd: a) 53.75% ofthe distribution's area? ' type your answer... l and [ type your answer... l b) 13.96% of the distribution's area? ' type your answer... ' and ' type your answer... ' c) 85.62% of the distribution's area? ' type your answer... ' and ' type your answer... ' d) 99.995% of the distribution's area? 1 type your answer... ' and ' type your answer... 1 point In a recent poll on world happiness, participants were asked to rate how happy they were on a scale of 0 to 10, with 0 being completely unhappy and 10 being incredibly happy. The mean response was 6.3, with a standard deviation of 1.9. a) What response represents the 90th percentile, rounded to one decimal place? ' type your answer... b) What response represent the third quartile, rounded to one decimal place? type your answer... 1 point The grade point average of a competitive school in recent years has a mean value of 3.36 and a standard deviation of 0.18. a) What is the lowest GPA, rounded to two decimal places, can a student hold and still be considered in the top 5%? I type your answer... b) A scholarship cut-off is the 80th percentile. What GPA must scholar recipients maintain? type your