The length of rose stems follows a normal distribution with a mean length of 19.15 inches and a standard deviation of 3.044 inches. A flower shop sells roses as parts of wedding flowers, wedding bouquets, and corsages. Please use this information to answer the following questions and please use R (not the z-table) for any calculations. a. What is the probability that a given rose stem will be shorter than 16.2 inches? Answer: Round to at least FOUR digits after the decimal if necessary. b. Suppose a rose is considered a 'long stem rose' if its stem length is longer than 24 inches. What is the probability that a given rose will be considered a long stem rose? Answer: Round to at least FOUR digits after the decimal if necessary. c. The flower shop has a rule that shortest 5% of roses are clipped and used as corsages. What is the maximum stem length (in inches) a rose can be and still qualify to be used as a corsage by the shop? Answer: inches. Round to at least FOUR digits after the decimal if necessary.

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