A. A manufacturer knows that their items have a normallydistributed length, with a mean of 19.7 inches, and standarddeviation of 4 inches.
If 25 items are chosen at random, what is the probability thattheir mean length is less than 17.4 inches?
Round to 4 decimal places

A manufacturer knows that their items have a normallydistributed lifespan, with a mean of 12.1 years, and standarddeviation of 1.9 years.
If you randomly purchase 12 items, what is the probability thattheir mean life will be longer than 11 years?
Round to 4 decimal places.

B. A company produces steel rods. The lengths of the steelrods are normally distributed with a mean of 98.4-cm and a standarddeviation of 0.9-cm. For shipment, 15 steel rods are bundledtogether.
Find the probability that the average length of the rods in arandomly selected bundle is between 97.9-cm and98.6-cm.
P(97.9-cm < X¯¯¯ < 98.6-cm)= Round to 4 decimal places.

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