(Total 6 marks) 8. Reaction times of human beings are normally distributed with

Question

(Total 6 marks) 8. Reaction times of human beings are normally distributed with a mean of 0.76 seconds and a standard deviation of 0.06 seconds. (a) The graph be low is that of the standard normal curve. The shaded area represents the robability that the reaction time of a person chosen at random is between 0.70 and 0.79 seconds. 0 b (i) Write down the value of a and of b. (i) Calculate the probability that the reaction time of a person chosen at random is (a) greater than 0.70 seconds; (b) between 0.70 and 0.79 seconds

Explanation / Answer

(i) Z = (X - mean) / standard deviation

Here a is the Z value corresponding to 0.70

Mean = 0.76 seconds

Standard deviation = 0.06 seconds

a = (0.7 - 0.76)/0.06 = -1

b = (0.79 - 0.76)/0.06) = 0.5

(ii) (a) P(X > 0.70) = P(Z > - 1)

= 1 - P(Z < - 1)

= 1 - 0.1587 (from standard normal for table)

= 0.8413

(b) P(0.7 < X < 0.79) = P(X < 0.79) - P(X < 0.7)

= P(Z < 0.5) - P(Z < 0.1587)

= 0.6915 - 0.1587

= 0.5328

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