Homework #1 Due Wednesday June 27th at 4 pm*Submit your homework on Canvas or to your TA’s mailbox before to the due date/time. The mailboxes areto the left as you enter the Medical Science Center (1300 University Ave.) from the main University Ave. entrance.*No late homework will be accepted for credit.*If a problem asks you to use R, include a copy of the code and output. Please edit your code and output tobe only the relevant portions.*If a problem does not specify how to compute the answer, you may use any appropriate method. I may askyou to use R or manual calculations on exam, so practice accordingly.1. If you wanted to estimate the mean height of all the students at a university, which one of the followingsampling strategies would be best? Why? Note that none of the methods are true simple random samples.(a) Measure the heights of 50 students found in the gym during basketball intramurals(b) Measure the heights of the engineering majors(c) Measure the heights of the students selected by choosing the first name on each page of a campus phonebook.2. A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phryno-soma were placed on a treatmill and their speed measured. The recorded speeds (meters/second) (the fastesttime to run a half meter) for the thirty lizards are summarized in the relative histogram below. (Courtesyof K. Bonine)1(a) Is the percent of lizards with recorded speed below 1.25 closest to: 25%, 50%, or 75%?(b) In which interval are there more speeds recorded: 1.5-1.75 or 2-2.5?(c) About how many lizards had recorded speeds above 1 meters/second?3. In a sample of 20 men, the mean height was 178 cm with standard deviation of 6 cm. In a sample of 30women, the mean height was 164 cm with standard deviation of 6 cm. If both samples were combined intoone larger group...(a) What is the mean height for the combined group?(b) The standard deviation for the combined group would be (hint: do not do any calculations, just try tosketch rough histograms for each sample separately and then one for the combined sample.)i. Less than 6 cmii. Greater than 6 cmiii. Equal to 6 cmiv. Can not tell from the information given4. After manufacture, computer disks are tested for errors. The table below gives the number of errors detectedon a random sample of 100 disks.Number of Defects 0 1 2 3 4Frequency 41 31 15 8 5(a) What is the shape of the histogram for the number of defects observed in this sample?(b) Calculate the mean and median number of errors detected on the 100 disks. How do these valuescompare and is that consistent with what we would guess based on the shape?(c) Calculate the sample standard deviation with your calculator and R. Are the values consistent betweenthe two methods? Explain what this value means in the context of the problem.(d) Calculate the first and third quartiles and IQR by hand and with R. Are the values consistent betweeenthe two methods? Explain what the three values mean in the context of the problem.(e) What proportion of the computer disks had a number of errors greater than the mean number of errors?2(f) What range of values for this sample data are not considered outliers using the [Q1-1.5IQR, Q3+1.5IQR]designation (using the IQR you calculated by hand)?.(g) Sketch a boxplot of the data by hand (using the relevant values you calculated by hand).5. Physical education researchers interested in the develoment of the overarm throw measured the horizontalvelocity of a thrown ball at the time of release. The results for first-grade children (in feet/sec) (courtesy ofL. Halverson and M. Roberton) are:Males: 54.2, 39.6, 52.3, 48.4, 35.9, 30.4, 25.2, 45.4, 48.9, 48.9, 45.8, 44.0, 52.5, 48.3, 59.9, 51.7, 38.6, 39.1,49.9, 38.3Females: 30.3, 43.0, 25.7, 26.7, 27.3, 31.9, 53.7, 32.9, 19.4, 23.7, 23.3, 23.3, 37.8, 39.5, 33.5, 30.4, 28.5(a) Use R to create a histogram for the males and a histogram for the females (any kind of histogram thatyou want). Adjust the x axis scale so the two groups are more easily compared.(b) Compare the shape of the throws from the male and female students observed in this sample.(c) Compute and compare the mean and median throw velocities observed in the male and famale studentsacross gender.(d) Compute and compare the standard deviation in throw velocities observed in the male and famalestudents.(e) Use R to help you create a boxplots of the two sets so they are easily comparable.(f) Which, if any values were identified as outliers? Would this value have been identified as an outlier ifit were thrown by the opposite gender?(g) What would be the shape of the histogram had we combined the boys and girls’ throw velocities intoone large data set (with 37 values)?6. A geologist weighs a specimen sample five times. The readings in grams are 48.5, 47.2, 4.91, 49.5, and 46.3.Which measures of center and spread will be highly affected by this outlier and thus give a clue that theyhave an entry error?7. A campus organization will select one day of the week for an end-of-year picnic. Assume that the weekdays,Monday through Friday, are equally likely and that each weekend day, Saturday and Sunday, is twice aslikely as a weekday to be selected.3(a) Assign probabilities to the seven outcomes.(b) Find the probability a weekday will be selected.8. Comparing observed data to a theoretical model.(a) Consider the simplistic model that human births are evenly distributed over the 12 calendar months(each person has an equal chance of being born in each month). If a person is randomly selected, sayfrom the phone directory, what is the probability that his or her birthday would bei. In a winter month (start of November-end of February)?ii. Not over the summer where summer is start of May-end of August?(b) The following record shows a classification of births (in thousands) in the United States. Calculate therelative frequency of births for each month and comment on the plausibility of a uniform probabilitymodel (each month has the same probability).Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec. Total331.5 309.6 349.3 332.5 346.3 350.9 357.1 369.3 363.4 344.6 335.7 348.3 4,138.59. The following frequency table shows the classification of 58 landfills in a state according to their concentrationof the three hazardous chemicals arsenic, barium, and mercury.If a landfill is selected at random, find the probability that it has:(a) A high concentration of barium.(b) A high concentration of mercury