A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.2 years, and standard deviation of 0.7 years. If you randomly purchase 5 items, what is the probability that their mean life will be longer than 2 years?
1.)A manufacturer knows that their items have a
If you randomly purchase 5 items, what is the probability that their mean life will be longer than 2 years?
Round to 4 decimal places.
2.)A particular fruit's weights are normally distributed, with a mean of 405 grams and a standard deviation of 14 grams.
If you pick 24 fruit at random, what is the probability that their mean weight will be between 399 grams and 410 grams.
Round to 4 decimal places.
3.)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 252.9-cm and a standard deviation of 2-cm. For shipment, 22 steel rods are bundled together.
Find P48, which is the average length separating the smallest 48% bundles from the largest 52% bundles.
P48 = cm Round to 2 decimal places.
4.)The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.904 g and a standard deviation of 0.289 g.
The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 42 cigarettes with a mean nicotine amount of 0.837 g.
Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 42 cigarettes with a mean of 0.837 g or less.
P(¯¯¯XX¯ < 0.837 g) =
Round to 4 decimal places.
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