36.7 seconds The amount of time to complete a physical activity in a PE class is

Question

36.7 seconds The amount of time to complete a physical activity in a PE class is normally distributed with a mean of and a standard deviation of 6.8 seconds. Round answers to 4 decimal places. a) What is the probability that a randomly chosen student completes the activity in less than 33.9 seconds? b) What is the probability that a randomly chosen student completes the activity in more than 45.5 seconds? c) What proportion of students take between 33.5 and 41.9 seconds to complete the activity? d) 90% ofall students finish the activity in less than seconds.

Explanation / Answer

A) P(X < 33.9)

= P((X - mean)/SD < (33.9 - mean)/SD)

= P(Z < (33.9 - 36.7)/6.8)

= P(Z < -0.41)

= 0.3409

B) P(x > 45.5)

= P((x - mean)/SD > (45.5 - mean)/SD)

= P(Z > (45.5 - 36.7)/6.8)

= P(Z < 2.29)

= 0.9890

C) P(33.5 < X < 41.9)

= P((33.5 - mean)/SD < (X - mean)/SD < (41.9 - mean)/SD)

= P((33.5 - 36.7)/6.8 < Z < (41.9 - 36.7)/6.8)

= P(-0.47 < Z < 0.76)

= P(Z < 0.76) - P(Z < -0.47)

= 0.7764 - 0.3192

= 0.4572

D) P(X < x) = 0.9

Or, P((X - mean)/SD < (x - mean)/SD) = 0.9

Or, P(Z < (x - 36.7)/6.8) = 0.9

Or, (x - 36.7)/6.8 = 1.28

Or, x = 1.28 * 6.8 + 36.7

Or, x = 45.404

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