Applied Statistics Final Spring 2026 Question Paper

Daffodil International University Department of Business Administration Course Title: Applied Statistics Course Code: STA - 202 Semester: Summer 202 5 Examination: Final Time: 2 Hou rs Full Marks: 40 Section: Retake Teachers’ Initial: ARE [NB: Answer all the following questions] Marks 01 a) Explain the conditions that must be satisfied to apply the Poisson probability distribution . 2 b) A commuter airline receives an average of 9.7 complaints per day from its passengers. Using the Poisson formula, find the probability that on a certain day this airline will receive at most 4 complaints also find Mean and Standard Devia tion . 6 02 a) Briefly explain the main characteristics of a norm al distribution. Illustrate with the help of graphs. 2 b ) Find the following probabilities for the standard normal curve with Figure s. i ) 𝑃 ( 1 . 19 < z < 2 . 12 ) ii ) 𝑃 ( − 1 . 56 < z < 2 . 31 ) iii) 𝑃 ( − . 75 < z ) 6 03 a) Explain the meaning of a point estimate and an interval estimate 2 b ) In a 2009 survey by I - Pension LLC, adults with annual household incomes of $50 , 000 𝑡𝑜 $125 , 000 were asked about the average time they spend reviewing their 401(k) statements. Of the adults surveyed, about 72% said that they spend less than 5 minutes, and 27% said that they spend 5 𝑡𝑜 10 minutes to review their 401(k) statements (USA TODAY, February 16, 2009). Suppose a random sample of 400 adults of all income levels who have 401(k) accounts were recently asked about the times they spend reviewing their 401 (k) statements. The sample pro duced a mean of 8 minutes. Assume that the standard deviation of such times for all 401(k) account holders is 2 . 20 minutes. Construct a 99% confidence interval for the mean time spent by all 401(k) account holders reviewing t heir 401(k) statements. 4 04 a ) Briefly explain the meaning of the degrees of freedom for a t distribution. Give one example. 2 b) Dr. Moore wanted to estimate the mean cholesterol level for all adult men living in Hartford. He took a sample of 25 adult men from Hartford and found that the mean cholesterol level for this sample is 186 mg/dL with a standard deviation of 12 mg/dL. Assum e that the cho lesterol levels for all adult men in Hartford are (approximately) normally distributed. Con struct a 95% confidence interval for the population M ea n . 4 0 5 a) Write down the steps of a test of hypothesis using the critical value approach . 2 b ) The TIV Telep hone Company provides long - distance telephone service in an area. According to the company’s records, the average length of all long - distance calls placed through this com pany in 2009 was 12 . 44 minutes. The 4