In its standardized form, the normal distribution a) has a mean of 0 and a stand

Question

In its standardized form, the normal distribution a) has a mean of 0 and a standard deviation of 1. b) has a mean of 1 and a variance of 0. c) has an area equal to 0.5. d) cannot be used to approximate discrete probability distributions. 2. For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is a) 0.18 b) 0.81 c) 1.16 d) 1.47 For some value of Z, the probability that a standard normal variable is below Z is 0.2090. The value of Z is a -0.81 b)-0.31 c) 0.31 d) 1.96 For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.1255. The value of X is a 0.99 b) 0.40 c) 0.32 d) 0.16 If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. a 0.3551 b) 0.3085 c) 0.2674 d) 0.1915

Explanation / Answer

1. a) has a mean of 0 and standard deviation of 1

2. c) P(X < Z) = 0.5+0.3770 = 0.8770

So, from standard normal distribution table, Z = 1.16 (option c)

3. P(X < X0) = 0.2090

Z value from  standard normal distribution table = -0.81 (option a)

4. P( 0 < x < 2X) = 0.1255

P(x < 2X) - P(0) = 0.1255

P(x < 2X) - 0.5 = 0.1255

P(x < 2X) = 0.6255

2X = 0.32

X = 0.16 (option d)

{Please post different questions separately}

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