1. Data collected over a long period of time showed that a particular genetic defect occurs in 2 of every 1000 children. Let X be the random variable “number of children with genetic defect in a sample of 20,000 children examined”. The records of a medical clinic show X = 25 children.

a) What is the probability of observing a value X of 25 or less?

b) Would you say that the observation of X = 25 children with genetic defect was rather unlikely?

please help it will be on test.
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

2 in 1000 gives a mean of 0.2%=0.002. In 20000 children µ, the mean, is 0.002*20000=40. So we would expect 40 cases in a sample size of 20,000.

a) Assuming a binomial distribution, in the absence of any other statistic, SD=√(20000*0.002*0.998)=6.32 approx. If we use this as σ in a normal distribution the z-score for X=25 is (25-40)/6.32=-2.37 corresponding to 0.0089 or 0.89%.

b) It is unlikely for X=25 given the mean and SD calculated.

by Top Rated User (600k points)

Related questions

0 answers
asked Nov 10, 2012 in Statistics Answers by anonymous | 870 views
2 answers
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,974 questions
86,370 answers
2,240 comments
71,894 users