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Good afternoon.  Any help with these questions would be greatly appreciated
Good afternoon. Any help with these questions would be greatly appreciated
Lesson 1 : Distribution of the sample m ean , sum, proportion and correlation. 1 | P a g e (1) Of the 7,500 students who attend classes at COSTAATT City Campus, 1,750 live in Diego Martin. On Monday 16th September 201 9, a sample of 400 students is surveyed from the COSTAATT City Campus student population, and 59 students said that they lived in Diego Martin. (a) What proportion o f Costaatt City Campus students live in Diego Martin? (b) On 17/09/2017 , what proportion of students said they lived in Diego Martin? (c) What is the Sampling error associated with our survey? (2) The balances of all savings accounts at a local bank have a distribution that is skewed to the right (you would’ve investigated this concept in STAT 120) with mean \$ 12,450 and s.d. of \$ 4,300. Find the probability that the mean balance of a sample o f 50 accounts will be more than \$ 11,500. (3) Graduate Management Aptitude Test (GMAT) scores are widely used by graduate schools of business as an entrance requirement. Every year more than two hundred thousand students from around the world attempt the exam. Suppose that in one particular year, the mean score for the GMAT was 850, with a standard deviation of 120. If a random sample of one thousand students (1,000) is chosen, what is the probability that their mean score is less than 847? (4) When a batc h of a certain chemical is prepared, the amount of a particular impurity in the batch is a random variable with mean value 4.0 g and standard deviation 1.5 g. If 50 batches are independently prepared, what is the (approximate) probability that the sample average amount of impurity is between 3.5 and 3.8 (5) At the XYZ Oil Company, the time it takes for new employees to learn how to operate the oil distribution machine has a mean 50 minutes and variance of 16 minutes. If a batch of new employees is being tr ained, what is the probability that the mean time taken for a sample of 45 employees is between 48 and 49 minutes? Lesson 1 : Distribution of the sample m ean , sum, proportion and correlation. 2 | P a g e (6) An unknown distribution has a mean of 90 and a standard deviation of 15. A sample of size 80 is drawn randomly from the population. (a) Find the probability that the sum of the 80 values (or the total of the 80 values) is more than 7,500. (b) Find the sum that is within 1.5 standard deviations of the mean of the sums. (7) An unknown distribution has a mean of 45 and a standard deviation of eight. A sample size of 50 is drawn randomly from the population. Find the probability that the sum of the 50 values is more than 2,400. (8) In a recent study reported on 18 th September, 2017 on the Flurry Blog, the mean age of Instagram users is 34 years. Suppose the standard deviation is 15 years. The sample of size is 50. (a) What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution? (b) Find the probability that the sum of the ages is between 1,50 0 and 1,800 years. (c) Find the 80th percentile for the sum of the 50 ages. (9) The mean number of minute s for app engagement by an iPhone user is 8.2 minutes. Suppose the standard deviation is one minute. Take a sample of size 70. (a) What are the mea n and standard deviation for the sums? (b) Find the 95th percentile for the sum of the sample. Interpret this value in a complete sentence. (c)_ Find the probability that the s um of the sample is at least 560 hours. Lesson 1 : Distribution of the sample m ean , sum, proportion and correlation. 3 | P a g e (10 ) 91% of the students, who have graduated from COSTAATT, r ated their COSTAATT experience as “Good” or “Excellent”. A random sample 500 students from the existing graduating class is selected. Let be the proportion of the COSTAATT students in the random sample who hold this view. (a) Describe the shape of the distribution of (b) Determine the parameters of (c) For another sample (also of size 500) determine the probability that . (11 ) It is known that 4 0% of the population of drivers in San Fernando exceeds the speed limit at least once per week. If 100 drivers are selected at random, what is the probability that more than 45 said they break the speed limit at least once a week? (12) It is known that 5 % of all students that do STAT 121 get an A. There are presently 55 students enrolled in STAT 121 this semester. What is the probability that more than 6 students will get an A this semester? (13 ) 20% of the students at secondary school in Trinidad and To bago dislike Mathematics. What is the probability that if 500 students are selected at random, less than 80 would like Mathematics? (14 ) For the academic year 2017/2018 the scores on the Mathematics admission exam and the English admission exam at Costaat t had a correlation coefficient of 0.6.If a sample of twelve students was chosen, what is the probability that the correlation between their scores (Math and English) was greater than 0.75 (15 ) The correlation between self estee m and extraversion is .30. A sample of 84 People is randomly selected . What is the probability that the co rrelation will be less than 0.25 ? (16 ) If the correlation between reading achievement and math achievement in the population of standard four studen ts is 0.60, what would be the probability that in a sample of 28 students, the sample correlation coefficient would be between 0.59 and 0.63 ? ^ P ^ P ^ P ^ 0.9 P     0.75 r

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