0. (3 points) The compressive strength of samples of concrete can be modeled by

Question

0. (3 points) The compressive strength of samples of concrete can be modeled by a normal dis- tribution with a mean of 2800 kilograms per square centimeter and a standard deviation of 95 kilograms per square centimeter. What strength is exceeded by 90% of the samples? a, 2921.7 kg/cm2 b. 2929.9 kg/cm2 786.2 kg/cm2 d. 14366.0 kg/cn2 e. 2936.8 kg/cm2 f. 2678.3 kg/cm2 1. (4 points) A short movie is scheduled to start at 10:00AM, 10:30AM, and 11:00AM. Once the movie starts, the doors will be closed. A visitor will arrive at the gate at a time uniformly distributed between 9:30AM and 11:00AM. The cdf of the time (in minutes) between 9:30AM and arrival is F(x) x/90, for 0 90. What is the probability that a visitor waits more than 10 minutes for a show? Express your answer to four decimal places. Ci 7

Explanation / Answer

Ans:

1)mean=2800

stadard deviation=95

P(Z>z)=0.9

P(Z<=z)=1-0.9=0.1

z=normsinv(0.1)=-1.282

x=2800-1.282*95

x=2678.3

option f is correct(2678.3)

2)

P(X<=x)=x/90

P(X>x)=1-(x/90)

P(X>10)=1-(10/90)=8/9=0.8889

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