NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(25, 0.05). (Round your probabilities to three decimal places.) (a) What are E(X) and σX? (Round your answers to two decimal places.) (b) In a sample of 30 children, what is the probability that none has a food allergy?

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 25 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(25, 0.05). (Round your probabilities to three decimal places.) (a) What are E(X) and σX? (Round your answers to two decimal places.) (b) In a sample of 30 children, what is the probability that none has a food allergy?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Let X and Y be the two possible events of an experiment where, p(X) = 0.5, P(XUY) = 0.9 and p(Y) = p. %3D (i) For what value of p are X and Y mutually exclusive ? (ii) For what value of p are X and Y independent ? CS Scanned with CamScanner
A recent study claims that 40% of registered voters associate themselves with Democrats. 35% with Republicans, 20% Independent, 3% Green party, and 2% with Social democrats. In a sample of 400 individuals, we observed 200 Democrats 150 Republicanse 25 Independente 15 Green Partye 10 Social Democrats Test the claim at a=0.05.e
Based on information from a previous study, r1 = 34 people out of a random sample of n1 = 105 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 = 105 adult Americans who did attend college, r2 = 50 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use ? = 0.01. (a) What is the level of significance?State the null and alternate hypotheses. H0: p1 = p2; H1: p1 ≠ p2H0: p1 < p2; H1: p1 = p2 H0: p1 = p2; H1: p1 < p2H0: p1 = p2; H1: p1 > p2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large.The Student's t. We assume the…
Hypertension It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample of 141 of each gender was selected from recent hospital records, and the following results were obtained. Can you conclude that a higher percentage of women have high blood pressure? Use α=0.05. Men 48 patients had high blood pressure Women 61 patients had high blood pressure Use p₁ for the proportion of men with high blood pressure and round all intermediate calculations to at least three decimal places. Part: 0 / 5 00 @ E 4 V olo
The probability of flu symptoms for a person not receiving any treatment is 0.032. In a clinical trial of a common drug used to lower cholesterol, 39 of 1137 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 39 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a). P(Xgreater than or equals 39)equals (Round to four decimal places as needed.)
Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)
In 1973, only 8% of the students in the city school district were classified as being learning disabled. A school psychologist suspects that the proportion of learning-disabled children has increased dramatically over the years. To demonstrate this point, a random sample of n = 13 students is selected. In this sample there are 3 students who have been identified as learning-disabled. You will use this information to determine if the sample indicates a change in the proportion of learning-disabled students at a 0.02 level of significance. Part 1: What is the hypothesized (assumed constant) population proportion for this test? p = (Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.) Based on the researcher's understanding of the situation, how many tails would this hypothesis test have? O one-tailed test two-tailed test
A sample of ?=14n=14 observations is drawn from a normal population with ?=1030μ=1030 and ?=200σ=200. Find each of the following: A. ?(?¯>1110)P(X¯>1110) Probability = B. ?(?¯<944)P(X¯<944) Probability = C. ?(?¯>997)P(X¯>997) Probability =
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Five hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%. Calculate the predictive value of a positive test.
The mean height of a certain kind of plant is 170 centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from 170. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test.
Hi Please assi
Suppose that having a widow's peak was a dominant trait (W) compared to not having a widow's peak (w). In a sample size of 30 students, 15 were observed to have a widow's peak and 15 did not have a widow's peak. The expected frequency of a widow's peak is 75% chance of getting it and a 25% chance of not getting it. Perform a chi square analysis to see if the data above agrees with the predicted outcome.