MA 203 DL Excel Project 2

Chapter 5 Skills- Probability Distributions/Binomial Cases

Gender Genetics

Given the following table,

1. Find the mean for the number of girl babies in eight births
2. Find the standard deviation for girls
3. Find the probability of getting exactly one girl in 8 births
4. Find the probability of getting 1 or fewer girls in 8 births
5. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births, the one in problem 3 or problem 4?
6. Is 1 a significantly low number of girls in 8 births? Why or why not?

# of Girls	P(x)
0	0.004
1	0.031
2	TIP: You can copy a table in this file and paste it into Excel to save typing. 0.109
3	0.219
4	0.273
5	0.219
6	0.109
7	0.031
8	0.004

Sleepwalking

The following table describes the numbers of adults in groups of five who reported sleepwalking, based upon data from "Prevalence and Comorbidity of Nocturnal Wandering in the US Adult General Population" (Ohayon et al, Neurology Vol 78, No20).

1. Find the mean for the number of sleepwalkers in groups of five
2. Find the standard deviation for the number of sleepwalkers in groups of five
3. Use the Range Rule of Thumb to determine whether four is a significantly high number of sleepwalkers in a group of five adults
4. Find the probability of getting exactly 4 sleepwalkers among 5 adults
5. Find the probability of getting 4 or more sleepwalkers among 5 adults
6. Which probability is relevant? Is 4 a significantly high number? Why or why not?

X	P(x)
0	0.172
1	0.363
2	0.306
3	0.129
4	0.027
5	0.002

Composite Sampling Examples

Problems 13 and 14 involve the method of composite sampling, whereby a medical testing lab saves time and money by combining blood samples for tests so that only one test is conducted for several patients. These samples tested positive so long as one patient is a carrier. If such a combined sample does test positive, individual tests are then used to identify the individual (or individuals) with the disease or disorder.

1. HIV- it is estimated that worldwide, 1% of those aged 15-49 are infected (circa 2016, data from the National Institutes of Health).In tests for HIV samples from 36 people are combined. A) What is the probability that the combined sample tests positive for HIV? B) Is it statistically unlikely for such a sample to test positive?
2. Anemia- Based on data from Bloodjournal.org, 10% of women 65 years of age or older have anemia (deficiency of red blood cells). If samples of 8 women in this age range are combined, A) What is the probability that the combined sample tests positive for anemia? B) Is it statistically likely for such a sample to test positive?

Aspirin Acceptance Sampling (Acceptance sampling is when a large shipment of items is accepted based upon the test results from a sample of the items shipped.) Suppose that the MedAssist Pharma Co receives large shipments of aspirin tablets with the following plan: Randomly select and test 40 tablets, accept the whole batch if one or none of the tablets fail to meet specified requirements.

1. If the current batch of 5000 tablets has a 3% defect rate, A) what is the probability that the whole shipment will be accepted? B) Will almost all such shipments be accepted, or will many be rejected?

Poisson Practice

1. Suppose that the NY- Langone Medical Center reported 4221 births in one year. A) Find the mean number of births per day B) Use the result from A to find the probability that in a single day there are 15 births C) Does it appear likely that on any given day there will be exactly 15 births?
2. Disease Cluster Example- Neuroblastoma normally occurs in 11 children per million (so the probability is 0.000011). Four cases of this cancer occurred in Oak Park Illinois, a town with 12,429 children. A) Assuming that neuroblastoma was occurring, as usual, find the mean number of cases in groups of 12.429 children. B) Using the UNROUNDED value from A, find the probability that the number of cases in a group that size is 0 or 1. C) What is the probability of more than one case of Neuroblastoma in a group of 12.429? D) Does the cluster appear to be attributable to chance? Why or why not?