The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. x 0 1 P(x) 0.1661 0.3306 0.2817 0.1484 0.0372 0.0360 2 3 4 5 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? E Click the icon to view the data tables. Compute the theoretical mean of the random variable X for the given probability distribution. Hx =O hits Data Tables (Round to three decimal places as needed.) Table of the numbers of hits for 25 games 2 1|3 3|5 4 212 IO 1 1 o1313 1 111 2 211 1 1 Table of the numbers of hits for 50 games 2 13 2 1 2 1

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 31 psi. A.  Pressure +31(27% of 31)= When tire pressure is below 22.63, the TPMS triggers a warning for the car. B.  Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning?  The probability the TPMS will trigger a warning Prob+P(X<=22.63); =P(X-u/a<=22.63-31/2); =P(z<=-4.185 Norm Distribution);  Probability=.00011 C.  The manufacturer’s recommended correct inflation range is 29 psi to 33 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range? Probability = ? I'd like to understand how to arrive at the answer. Thank you!

The lifetime of a particular brand of AA batteries follows a normal distribution. The mean lifetime of particular brand of AA batteries is 1000 hours, with a standard deviation of 100 hours. What is the probability that a randomly selected battery lasts more than 875 hours?     Select one: a. 0.8716 b. 0.3749 c. 0.1056 d. 0.8944

a physical fitness association is including the mile run in its secondary school test. the time for this event for girls in the secondary school is known to posses a normal distribution with the mean of 450 seconds and standard deviation of 59 seconds. find the probability that a randomly selected girl in secondary school will take longer than 335 seconds to run the mile A. 0.5107 B. 0.9893 c. 0.0107 D. 0.4893

Measuring success as the ratio of runs/at-bats makes sense. Suppose the mean ratio for the league is 0.200 and is normally distributed with a standard deviation of 0.01. How could a manager apply the normal probability distribution (for recruiting) to determine if it is unusual that a random player has a ratio of 0.220?

Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is greater than 8?

Find the probability that the mean volume of soft drink in the 25 sampled bottles is less than 15.4 ounces. (Give your answer to four decimal places) Find the probability that the mean volume of soft drink in the 25 sampled bottles is more than 15.5 ounces. (Give your answer to four decimal places)

Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is less than 8?

Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?

A surgery has a success rate of 90%. Suppose that the surgery is performed on threepatients Graph the probability distribution for X using a histogram.Find the mean of X.Find the variance and standard deviation of X.