Assignment # 3
Last Name ——————————————- , Student # ———————— Lab section (Important) ———————– Due in class: Tue. Nov. 12
Total mark=100. Marks for each question are given in [ ] Part I. Lab questions. Use only blanks left to answer lab questions. Provide all histograms you are asked to print, but DO NOT print data you are asked to generate. 1. Continuous distributions: Generate and store in column c1 10,000 values from the uniform distribution on the interval [3,7] as follows: random 10000 c1; uniform 3 7.  a. Use mean command to ﬁnd the sample mean x of these data———————– ¯  b. What is the mean µ of the uniform distribution on the ...view middle of the document...
What are the mean µ————– and the standard deviation σ————– of the standard normal distribution? 1
3. Standardization procedure: Generate and store in column c4 10,000 values from the normal distribution with µ = 6.5 and σ = 3 as follows: random 10000 c4; normal 6.5 3. a. Print (and include in your assignment) the histogram for these data . What is the value on the horizontal axis around which the histogram seems to be symmetric?x =—— Construct and store in column c5 the data set zi (i = 1, . . . , 10, 000) obtained from the previously generated data set xi by the standardization procedure zi = (xi − µ)/σ by typing: let c5=(c4-6.5)/3 b. Print (and include in your assignment) the histogram for the zi s . Around which value does it seem to be symmetric?—— What are the sample mean and standard deviation: z and s for this new data set?——————- and ——————– Why are they close ¯ to 0 and 1 (respectively)?—————- 4. Central limit theorem (CLT) at work (You can use a new Minitab worksheet). Generate and store in columns c3-c902 100 samples, of size n = 900 each, from exponential distribution with mean 9 as follows: random 100 c3-c902; exponential 9. Note This may take a few moments as you are generating 900x100=90,000 values Create and store in column c1 the 100 values of x based on the 100 samples of same size ¯ n = 900 as follows: rmean c3-c902 c1 a. Print (and include in your assignment) the histogram of c3 . What can you conclude about the shape of this data set?————–  b. Use desc command to ﬁnd sample mean and sample standard deviation of c3——— ———————————————–  c. Print (and include in your assignment) the boxplot for the data in column c1. What can you conclude about the shape of the data in c1?———————— d. Use desc to ﬁnd sample mean and sample standard deviation of c1——- and ——-. Are they close to 9 and 9/30 (respectively)?———————– Why?———————— ——————————————————————————————————— Part II. Long-answer questions 1. Data collected over a long period of time showed that a particular genetic defect occurs in 1 of every 1000 children. Let X be the random variable “number of children with genetic defect in a sample of 50,000 children examined”. The records of a medical clinic show X = 60 children.  a. What is the probability of observing a value of X equal to 60 or more?  b. Would you say that the observation of X = 60 children with genetic defect was rather unlikely? 2. Suppose a random sample of n = 36 observations is selected from a population that has normal distribution with mean 106 and standard deviation 12. ¯  a. Give the mean and the standard deviation of the sample mean X. ¯  b....