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Chapter 6: Problem 16
Determine the following probabilities for the standard normal distribution. a. \(P(-1.83 \leq z \leq 2.57)\) b. \(P(0 \leq z \leq 2.02)\) c. \(P(-1.99 \leq z \leq 0)\) d. \(P(z \geq 1.48)\)
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What is the difference between the probability distribution of a discrete random variable and that of a continuous random variable? Explain.
The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $$\$ 95$$ and a standard deviation of $$\$ 20.$$ If the management wants to give free gifts to at most \(10 \%\) of the customers, what should the amount be above which a customer would receive a free gift?
A company that has a large number of supermarket grocery stores claims that customers who pay by personal checks spend an average of $$\$ 87$$ on groceries at these stores with a standard deviation of $$\$ 22 .$$ Assume that the expenses incurred on groceries by all such customers at these stores are normally distributed. a. Find the probability that a randomly selected customer who pays by check spends more than $$\$ 114$$ on groceries. b. What percentage of customers paying by check spend between $$\$ 40$$ and $$\$ 60$$ on groceries? c. What percentage of customers paying by check spend between $$\$ 70$$ and $$\$ 105 ?$$ d. Is it possible for a customer paying by check to spend more than $$\$ 185$$ ? Explain.
Determine the value of \(z\) so that the area under the standard normal curve a. in the right tail is \(.0500\) b. in the left tail is \(.0250\) c. in the left tail is \(.0100\) d. in the right tail is \(.0050\)
Tommy Wait, a minor league baseball pitcher, is notorious for taking an excessive amount of time between pitches. In fact, his times between pitches are normally distributed with a mean of 36 seconds and a standard deviation of \(2.5\) seconds. What percentage of his times between pitches are a. longer than 39 seconds? b. between 29 and 34 seconds?
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