Consider a binomial distribution with n=23 fixed trials and probability of success p=0.14. Let r be be the number successes. find the expected value (μ) and the standard deviation (σ) of r. (Round your answers to two decimal place.) μ= σ=

At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of µ = 9 pounds with a standard deviation of σ = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected, and the average weight change is computed for the sample. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)? (four decimals)

I'm having a hard time on this question. A single toss of a fair coin results in either 0 or 1 head, each with probability 1/2. Define H = number of heads obtained on a single toss. The mean of H is = 0.5 And the standard deviation of H is = 0.5. Suppose you toss a fair coin four times. Define T = total number of heads obtained. Find the mean and standard deviation of T.

Assume that adults have IQ scores that are normally distributed with a mean of μ= 105 and a standard deviation o=15. Find the probability that a randomly selected adult has an IQ less than 123. Click to view page 1 of the table Click to view page 2 of the table. The probability that a randomly selected adult has an IQ less than 123 is (Type an integer or decimal rounded to four decimal places as needed.). THE

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1522 and the standard deviation was 311. The test scores of four students selected at random are 1950, 1260, 2190, and 1410. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1950 is. (Round to two decimal places as needed.)

A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1539 and the standard deviation was 315. The test scores of four students selected at random are 1940, 1290, 2240, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1940 is. (Round to two decimal places as needed.) The Z-score for 1290 is. (Round to two decimal places as needed.) The Z-score for 2240 is. (Round to two decimal places as needed.) The Z-score for 1420 is. (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The unusual value(s) is/are. CD (Use a comma to separate answers as needed.) OB. None of the values are unusual.

Assume that adults have IQ scores that are normally distributed with a mean of u =100 and a standard deviation o = 15. Find the probability that a randomly selected adult has an IQ less than 115. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ less than 115 is (Type an integer or decimal rounded to four decimal places as needed.)

The mean weight of all Goliath grouper caught on the Treasure coast is 367 pounds, with a standard deviation of 33 pounds. Suppose a random sample of 32 Goliath Grouper from the Treasure Coast are caught and weighed. Determine the probability that the average weight of the sample of 32 Goliath Grouper is within 7 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places , if necessary .

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P70, the 70-percentile. This is the temperature reading separating the bottom 70% from the top 30%.P70 = °C(Round answer to three decimal places)