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.4. population of values has a normal distribution with p. = 143.3 and or = 92.3.'1'ou intend to draw a random sample of sizes; 2 49. a. Find the probability that a single randomly selected value is less than 144.3. PIX 144.31: :l Round to 4 decimal places. b. Find the probability that the sample mean is less than 144.3. FLT 144.31: C] Round to 4 decimal places. Answers obtained using exact zscores or z-scores rounded to 2 decimal places are accepted. A manufacturer knows that their items have a normally distributed length, with a mean of 6.6 inches, and standard deviation of 1.4 inches. If 24 items are chosen at random, what is the probability...r that their mean length is less than 6.? inches? Round to 4 decimal places. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.1 years, and standard deviation of 1.1 years. If you randomly purchase 7 items, what is the probability that their mean life will be longer than 6 years? Round to 4 decimal places.A particular fruit's weights are normally distributed, with a mean of 555 grams and a standard deviation of 36 grams. If you pick 5 fruit at random, what is the probability that their mean weight will be between 508 grams and 603 grams. Round to 4 decimal places.A com pan}.r produces steel rods. The lengths of the steel rods are normally distributed with a mean of 234.3cm and a standard deviation of1.5cm. For shipment. 12 steel rods are bundled together. Find P22. which is the average length separating the smallest 22% bundles from the largest ?8% bundles. P22 = C] cm Round to 2 decimal places. The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.886 g and a standard deviation of 0.295 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 32 cigarettes with a mean nicotine amount of 0.803 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 32 cigarettes with a mean of 0.803 g or less. P(X