Standard Deviation and Random Sample

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Problem Sheet - I

1. Researcher conducted by a tobacco company indicates that the relative frequency distribution of tar content of its newly developed low-tar cigarette has a mean equal to 3.9 milligrams of tar per cigarette and a standard deviation equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true, what is the probability that the mean tar content of the sample is greater than 4.15 milligrams? [0.00621]

2. The safety limit of a crane is known to be 32 tons. The mean weight and the standard deviation of a large number of iron rods are 0.3 ton and 0.2 ton respectively. One hundred rods are lifted at a time. Compute the probability of an accident. [0.1587]

3. A soft –drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 milliliters and a standard deviation of 15 milliliters. What is the probability that the mean amount dispensed in a random sample of size 36 is at least 204 milliliters? [0.0548]

4. An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean (μ) = 117 cm and standard deviation (σ) = 6.1 cm. Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm. [0.16354]

5.The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3. What is the probability that in a random sample of 25 students, more than 275 pizzas are consumed? [0.04746]

6.The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers...
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