1. In a particular facility, 60% of students are men and 40% are women. In a random sample of 50 students what is the probability that more than half are women?
Let the random variable X = number of women in the sample.
Assume X has the binomial distribution with n = 50 and p = 0.4.
1. In a particular facility, 60% of students are men and 40% are women. In a...
If x is a binomial random variable where n = 100 and p = 0.30, find the probability that x is greater than or equal to 35 using the normal approximation to the binomial. (Discuss whether continuity correction is required or not)
5. (20 pts) Suppose on a given college campus 45% of the students own an iPhone, 50% an Android smartphone and 5% some other type of phone. Let X=the number of students in a simple random sample of 15 students who own an iPhone. A. What is the probability distribution of X? Note: If this is a well-known distribution it is sufficient to name the distribution and identify the value of the parameters B. Find the probability that 8 students...
If Y is a binomial random variable with parameters n=60 and p=0.5, estimate the probability that Y will equal or exceed 45 using the Normal approximation with a continuity correction.
40 women and 60 men have been selected to complete a survey on political preferences. Suppose half of the women are Conservative and half of the men are Conservative. Suppose one individual is chosen randomly from the sample. What is the probability that it is anybody other than a Conservative man?
11 0067 Normal approximation to Binomial Pages 299-305 a. School officials claim that about 13.5% (This is p) of the students who take out overnment backed loans to pay for college tuition default on their payments. What is the probability that a sample of 132 (this is n randomly selected students who have taken out government-backed loans will contain at most 111 students who will pay back their loan (ie, will not default)? Remember to use the correction for continuity....
Suppose that the number of asbestos particles in a sample of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared centimeters of dust contains more than 10030 particles? Use normal approximation without continuity correction. Round your answer to 3 decimal places
Question 1 (Normal Approximation). Suppose that 25% of Rackham graduate students are Graduate Student Instructor (GSI). Now, select a random sample of 50 Rackham graduate students. Let X be the number of Rackham graduate students in the random sample who are GSI. (a) What is the distribution of X? (b) Approximate X using a normal random variable Y and provide the mean and variance of Y. Explain all the required conditions for this approximation (c) What is the approximate probability...
4.- In a certain university, 20% of men and 1% of women measure more than 1.75 m. of height. Also, 42% of the students are women. If a student is selected at random and it is observed that he is 1.68 m tall, what is the probability that he is a man? Round to 4 decimals.
Suppose that 14% of the people in a large city have used a hospital emergency room in the past year. If a random sample of 125 people from the city is taken, approximate the probability that fewer than 19 used an emergency room in the past year. Use the normal approximation to the binomial with a correction for continuity.
Part B Q5. [6] 64% of Ball State University students are inter-state students. If we observe 100 students at random, use the normal approximation to find the probability of observing (a) more than 70 inter-state students. (b) not more than 50 inter-state students.