The area under the normal curve between z = 0 and z =1 is the area under the nor

Question

The area under the normal curve between z = 0 and z =1 is the area under the normal curve between z =1 and z = 2. a) less than b) equal to c) greater than d) dependent on the value of the mean for If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour a) is greater than the proportion of workers earning less than $13 per hour. b) is greater than the proportion of workers earning less than $18 per hour. c) is less than the proportion of workers earning more than the mean wage. d) is less than 50%. For some value of X, the probability that a standard normal variable is between 0 and X is 0.3770. The value of X is: a) 0.18 b) 0.18 or - 0.18 c) 1.16 or - 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 Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. a) 0.0440 b) 0.1915 c) 0.4552 d) 0.9104

Explanation / Answer

3. a) greater than

4. a) is greater than the proportion of workers earning less than $13 per hour

5. c) 1.16 or -1.16

6. a) -0.81

7. mean = 50

standard deviation = 2

P(X is between 47 and 54) = P(X<54) - P(X<47)

= P(Z <(54-50)/2) - P(Z <(47-50)/2)

= P(Z < 2) - P(Z < -1.5)

= 0.9772 - 0.0668

= 0.9104

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