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A consumer organization that evaluates new motorcycles customarily reports the number of major defects in each motorcycle examined. Let X denote the number of major defects in a randomly sellected motorcycle of a certain type. Recall the cunulative density function, or cof, is a function for x that calcuilates t The cdf of X is as follows the probability of the value x and all values below, F(x) Prxsx) Fx) 0.02 0.22 0.36 0.60 0.89 0.97
Calculate the following probabilities directly from the cdf: (Round to two decimal places.) ( (a) F(2), that is, P X S 2) (b) P(X> 3) (c) P(2 SXS 5) (d) P(2<X<5) (e) what is the probability mass function, p(X-x), for x? (Round to two decimal places.) p(x) (f) The mean and standard devilation for X are: (Round to two decimal places.) 5 The average number of defects is, E(x) The number of defects deviate from the average by, sDx)
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(c) The probability that the random variable X is between 2 and 5 is F(S)-F(2) → 0.97-0.36 0.61 P(2sXs5) 0.61 Therefore, the probability that the random variable X is between 2 and 5 is P(2sXs5)04 (d) The probability that the random variable X is between 2 and 5is 0.89 0.22 0.67 P(2 <X <5)0.67 Therefore, the probability that the random variable X is between 2 and 5 is P(2 <X <5) 0.67

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