Problem 1A. Suppose that a sample of 189 babies are found to have birth weights with approximately a normal distribution, having mean 2945 grams and standard deviation 729 grams.
Using this normal distribution as a probability model, what fraction of babies are predicted to have birth weights of less than 2500 grams?(Answer up to 2 decimal places)
Problem 1B. Using library(MASS); attach(birthwt); and ecdf(birthwt$bwt), what fraction of babies in the birthwtdata frame have birth weights of at most 2500 grams? (Answer up to 2 decimal places)
Problem 2.On average, two tornadoes hit major U.S. metropolitan areas every year. What is the probability that more than four tornadoes occur in major U.S. metropolitan areas next year?(Answer up to 5 decimal places)
Problem 3. Suppose that an employee will make a transition to one of three possible next states, Quit, Promoted, Laid Off, as follows:
–Quit: rate = 0.5 per year
–Promoted: rate = 0.8 per year
–Laid off = 0.2 per year
What is the probability that the employee quits before being promoted or laid off? (Answer up to two decimal places)
Problem 4. Ten percent of computer parts produced by a certain supplier are defective. What is the probability that a sample of 10 parts contains more than 3 defective ones?
(Answer up to 6 decimal places)
Problem 5. Suppose that 2 successes are observed in 10 binomial trials
Use the binom.confint() function in package binom to find an exact 95% upper confidence limit (UCL) for the success probability, p.
–If needed, install package binom first using install.packages(“binom”)
Using library() will show if installation is needed
Remember to use library(binom) before using binom.confint() (i.e., activate package before trying to use its functions
(Answer up to 4 decimal places)
Problem 6. Load the Boston dataset in package MASS
–Hint: Similar to loading survey data frame in the example
What is the median value of the age variable in this dataset?
–Hint: Median value of the age variable in the survey data set was 18.58
(Answer up to two decimal places, for eg., 12.50)