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Z-Score and Probability

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1: Given the standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in table E.2), what is the probability that
A: Z is less than 1.57?
B: Z is greater than 1.84?
C: Z is between 1.57 and 1.84?
D: Z is less than 1.57 or greater than 1.84?

2: The breaking strength of plastic bags used for packaging produce is normally distributed, with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. What proportion of the bags have a breaking strength of
A: less than 3.17 pounds per square inch?
B: at least 3.6 pounds per square inch?
C: between 5 and 5.5 pounds per square inch?
D: 95% of the breaking strengths will be contained between what two values symmetrically distributed around the mean?

3: A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed, with the mean = 240 seconds and the standard deviation = 40 seconds.
A: What is the probability that a call lasted less than 180 seconds?
B: What is the probability that a call lasted between 180 and 300 seconds?
C: What is the probability that a call lasted between 110 and 180 seconds?
D: What is the length of a call if only 1% of all calls are shorter?

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  • BSc, Banaras Hindu University
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