Scores on a standardized reading test for fourth-grade students form a normal distribution with μ = 71 and σ = 24. What is the probability of obtaining a sample mean greater than M = 63 for each of the following: a sample of n=36?

For a standard normal distribution, what is the probability that z is greater than 1.75?

1. 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

3. 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

4. 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

5. 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 35. minutes and a standard deviation of 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 

Assuming that the thermometer readings have a normal distribution with a mean of 0 °C and a standard deviation of 1 °C, what is the probability of getting a reading between 1.50 and 2.25?