Ship collisions in the Houston Ship Channel are rare. Suppose of collisions are Poisson distributed, with a mean of 1.2 collisions every four months. What is the probability of having one or less collision over a four-month period? Round you answer to 3 decimal places.

Random samples of a Gaussian distribution will fall within two standard deviations of the mean with a probability which is approximately 68%. True or False

The expected relative frequency of a particular outcome is?

( Question 3 A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. 3-' a. Find the probability that exactly 14 survive. survive. b. Find the probability that at least 10 c. Find the probability that at most 6 lethal. d. Find the mean and variance of the number that survive. (~210 n-20

# 3. Use Minitab to simulate 1000 rolls of five dice. Find the number of times that the sum of the five dice is exactly 20. Enter that value here. frequency approach to estimate the probability of getting a 20 when five dice are rolled. Enter the estimated probability here. Based on that result, use the relative Write a sentence or two explaining the difference (advantage or disadvantage) of the classical approach to probability compared to the relative frequency approach to probability. Refer to the results from #1, 2, 3 above in your explanation.

Mensa requies a test score to be in the top 2%. The test has a mean of 100 and Std. Dev. of 15.and scores are normally distributed. If 4 subjects take the test and they have a mean of 132 but the individual scores are lost, can we conclude that all 4 of them are eligible for Mensa?

If Y is a random variable from an exponential distribution with a mean of 5; what is the probability that Y is more than 7?

TREKLAIR bulbs have an average lifespan of800 hours with a variance of 1,600 hours2 .This duration oflife has a normal distribution. Find the probability that abulb lasts between 778 and 834 hours.

Does playing Mozart for unborn babies result in having children with higher IQs?    A psychologist obtains a random sample of 30 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 45 minutes each day until they give birth. We know that IQs are normally distributed with a mean of 100.    A few years after their births the children were given an IQ test and the IQs of the 30 children in the study resulted in a sample mean of 104.2. Assume the population standard deviation for IQ of children is 15.    Is there evidence that the children who listen to Mozart for at least 45 minutes each day during pregnancy have higher IQs at the 0.05 level of significance? Use the p-value approach. a. Define the parameter we are testing and setup a hypothesis test to see if the mean IQ of children who listened to Mozart at least 45 minutes a day during pregnancy is higher than the national mean of 100: b. Calculate the test statistics for this…

Question 5 > About 62% of people who are murdered knew the person who committed the murder. Suppose that Detective Moore's case load currently has 50 unsolved murders. Use a normal distribution approximation to the binomial distribution to find the following probabilities: a. What is the probability that no more than 28 of the victims among Detective Moore's case files knew their murderer? b. What is the probability that between 28 and 34 of the victims knew their murderer?