![]() ![]() To do this, we will compare what we actually observe with what we would expect to observe if the geometric model were correct. We will investigate whether the variables "NumtoB" and "NumtoG" really do follow approximately a geometric distribution with p = 1/2. The fifth baby was the previous girl, but then we had to wait for four more babies (numbers 6, 7, 8, and 9) to get the next girl. To understand how these variables were computed from the "Gender" variable, consider, for example, the ninth baby, which was a girl. How many boys and how many girls are there in the data set?Now consider the variables "NumtoB" and "NumtoG".In Minitab Express, the command is Statistics -> Summary Statistics -> Tally This command will be useful throughout the lab. Minitab outputs how many times each value (in this case B or G) appears in the column. We will first do a quick check to see if boys and girls appear to be equally likely.Go to Stat -> Tables -> Tally Individual Variables, select the variable "Gender", and click "OK". If we assume that each baby in our data set is independently a boy or a girl with probability 1/2 each, then the number of babies that are born before the next boy (or girl) should have the geometric distribution with p = 1/2. If a baseball player gets a hit 30 percent of the time that he bats, the number of times that he bats before getting a hit has the geometric distribution with p = 0.3. The number of times we have to toss a coin before we get a head has the geometric distribution with p = 1/2. Then the number of trials that it takes to get a success has the geometric distribution with parameter p. Suppose we have independent Bernoulli trials, each resulting in success with probability p and failure with probability 1 - p. Waiting for boys or girls (Geometric Distribution) The number of births in the data set on that day The length of time, in hours, since the previous birth The number of the previous four babies born that were girls The time of the day that the baby was born, measured in hours after midnightįor boys, the number of births (including the current one) since the previous boyįor girls, the number of births (including the current one) since the previous girl The last two columns have 182 rows and give the number of babies born on each of the 182 days between and. The first eight columns have 290 rows and provide information about each of the 290 babies. The data set includes the following columns. Twins were also excluded from the data set. A few babies for which the gender could not be determined from the name, or other information was unavailable, were excluded from the data set. Information at the Baby Name Facts web site was used to help with distinguishing male and female names. The data were obtained from the WebNursery web site. We have data on 290 babies born at Saddleback Memorial Medical Center in Laguana Hills, California during the months of January through June, 2008. Click here for a one-page handout reviewing these six distributions.įirst, open the data set BABIES, which is available in Canvas. In the course, we have introduced six different probability distributions: geometric, binomial, Poisson, uniform, exponential, and normal. One goal of this lab is to help you gain experience in determining when you should expect to see different probability distributions arising in practice. Math 11, Lab 5 Lab 5: Birth times and birth weights (Probability distributions)In this lab, you will investigate the genders, birth times, and birth weights of babies. ![]()
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