Q 2/ In a certain city, the number of power outages per month is a random variable, having a distribution with n =22 and p = 0.7. If this distribution can be approximated closely with normal distribution, what is the probability that there will be 11 or more outages in any one month?
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- Suppose that you make a large number of independent observations of a random variable and then construct a table giving the possible values of the random variable and the proportion of times each value occurs. What will this table resemble?A tube of listerine tartar control toothpaste 4.2 ounces. As people use the toothpaste the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. What is the probability that there is more than 1.5 ounces remaining in the tube?After careful research you observe that the number of hackers active on each day is a random variable Bin(3,0.5) distribution. If no hackers are active, the probability of the website failure is 0.15; If one hacker is active the probability of the website failure is 0.3; if two or more hackers are active the probability of the website failure is 0.5. You conclude that the total probability of website failure on a given day is two decimal place). Assuming there is a failure, the probability no hackers are active is (to (to two decimal places).
- Average temperatures in May in a certain city are normally distributed with a mean of 70 degrees and a standard deviation of 6 degrees. If one random day in May is selected, what is the probability that the temperatures will be above 85 degrees?Suppose 2 dice are rolled, and suppose the discrete variable x counts the number of 3’s that show up. Plot the probability distribution for x using a bar graph. What is the expected value for the random variable x? What is the variance for the random variable x?Suppose a set of 100 random numbers is normally distributed, with a mean of 50 and standard deviation 2. What is the probability of leaving the number 50?
- Assume that your aunt wrote 139 letters to her family members in 2019. Let the random variable x represent the number of these letters that she wrote on a given day. Assume also that this scenario has a Poisson distribution. What is the mean number of letters written per day? Round to 3 decimal places. What is the standard deviation? Round to 3 decimal places.If Y is a random variable with a mean of 30 and a standard deviation of 10, what is the probability that Y is between 35 and 40?Suppose the weight of turkeys in a store are normally distributed with mean 15.5 lb and standard deviation 2 lb. If a turkey is grabbed at random what is the probability that the weight will be less than 16 lb?
- Each trial in a binomial experiment has a 25% probability of success.if the normal distribution is to be used to calculate a probability for thisbinomial experiment, then number of trials must be at leastSuppose our random variable is the braking distance of a certain car in feet on a dry surface when going 55mph. The mean braking distance is 148 feet and the standard deviation is 2.64 feet. We randomly sample 33 braking distances from this population, what is the probability that the mean braking distance for the sample is between 147.6 feet and 150 feet?* Your answer is incorrect. Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 2 customers in the first line and n₂ = 13 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.1 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i 98.80