The random variable X, representing the number of cherries in a cherry puff, has the probability...

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The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. P(X=x)+ 5 0.2 6 7 8 0.4 0.3 0.1 Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the mean and the variance o of X. =(Type an integer or a decimal. Do not round.) a=(Type an integer or a decimal. Do not round.) (b) Find the mean g and the variance of the mean X for random samples of 49 cherry puffs. HX (Type an integer or a decimal. Do not round.) (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 49 cherry puffs will be less than 6.5. The probability is. (Round to four decimal places as needed.) The random variable X, representing the number of cherries in a cherry puff, has the probability distribution shown. P(X=x)+ 5 0.2 6 7 8 0.4 0.3 0.1 Complete parts (a) through (c) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the mean and the variance o of X. =(Type an integer or a decimal. Do not round.) a=(Type an integer or a decimal. Do not round.) (b) Find the mean g and the variance of the mean X for random samples of 49 cherry puffs. HX (Type an integer or a decimal. Do not round.) (Round to three decimal places as needed.) (c) Find the probability that the average number of cherries in 49 cherry puffs will be less than 6.5. The probability is. (Round to four decimal places as needed.)