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An analogue signal received at a detector, measured in micro volts, is normally distributed with mean of 200 and variance of 256

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An analogue signal received at a detector, measured in micro volts, is normally distributed with mean of 200 and variance of 256.

(a) What is the probability that the signal will exceed 224 ????V?

(b) What is the probability that it will be between 186 and 224 ????V?

(c) What is the micro voltage below which 25% of the signals will be? d) What is the probability that the signal will be less than 240 ????V, given that it is larger than 210 ????V?

(e) Estimate the inter quartile range.

(f) What is the probability that the signal will be less than 220 ????V, given that it is larger than 210 ????V?

(g) If we know that a received signal is greater that 200 ????V, what is the probability that is in fact greater than 220 ????V?