Question

1. Suppose the variable x is represented by a standard normal distribution.

What is the probability of x < -0.6?

Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

2. Suppose the variable x is represented by a standard normal distribution.

What value of x is at the 90th percentile of the distribution? Equivalently, what is the value for which there is a probability of 0.90 that x will be less than that value?

Please round your answer to the nearest hundredth.

3.Major league baseball game durations are normally distributed with a mean of 150 minutes and a standard deviation of 35 minutes.

What is the probability of a game duration of between 170 and 200 minutes?

Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).

Answer 1

1) This is a normal distribution question with

z = -0.6
This implies that
P(z < -0.6) = 0.27
2) Given in the question
P(X < x) = 0.9
This implies that
P(Z < 1.28) = 0.9

z = 1.28
you have to refer z score table to find the final probabilities.

3) This is a normal distribution question with

P(170.0 < x < 200.0)=?

This implies that
P(170.0 < x < 200.0) = P(0.5714 < z < 1.4286) = P(Z < 1.4286) - P(Z < 0.5714)
P(170.0 < x < 200.0) = 0.92 - 0.72
P(170.0 < x < 200.0) = \textbf{0.20}
PS: you have to refer z score table to find the final probabilities.
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