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[-3] Compute and interpret the mean of the random variable x. The mean is El activities. (Type an integer or a decimal. Do not round.) Which of the following interpretations of the mean is correct? 0 it. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable. 0 B. The observed value of an experiment will be less than the mean of the random variable in most experiments. 0 C. As the number of experiments increases, the mean of the observations will approach the mean of the random variable. 0 D. The observed value of an experiment will be equal to the mean of the random van'able in most experiments. [d] Compute the standard deviation of the random variable x. The standard deviation is D activities. [e] What is the probability that a randomly seleded student has a parent involved in three activities? The probability is . (Type an integer or a decimal. Do not round.) [ What is the probability that a randomly selected student has a parent involved in three or tour activities? The probability is . (Type an integer or a decimal. Do not round.) In the following probability distribution, the random variable x represents the number of activities a parent of a K to 5th-grade student is involved in. Complete parts (a) through (f) below. X 0 P(x) 0.092 0.202 0.268 0.075 4 0.363 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because the sum of the probabilities is ] and each probability is (b) Graph the discrete probability distribution. Choose the correct graph below. O A. greater than or equal to 0. OB. between 0 and 1, inclusive. 0.5- OD. 0.4- 0.5- less than or equal to 1. 0.4- 0.57 0.3- 0.3- greater than 0 and less than 1. 0.4- 0.2- 0.3- 0.2-A lab orders a shipment of 100 rats a week, 52 weeks a year, for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below. How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.) Price $10.00 $12.50 $15.00 Probability | 0.35 0.3 0.35 O $650.00 O $3,380,000.00 O $1,250.00 O $12.50The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 2% of its customers, how long should it make the guaranteed time limit? Click here to view the standard normal distribution table (page 1)_ Click here to view the standard normal distribution table (page 2)_ (a) The percent of customers that receive the service for half-price is% (Round to two decimal places as needed.) (b) The guaranteed time limit is |minutes. (Round up to the nearest minute.)