The length of rose stems follows a normal distribution with a mean length of 19.31 inches and a standard deviation of 3.02 inches. A flower shop sells roses as parts of wedding flowers, wedding bouquets, and corsages.

Please use this information to answer the following question, and use R (not the z-table) for any calculations.

a. What is the probability that a given rose stem will be shorter than 16.7 inches?

To find the probability that a given rose stem will be shorter than 16.7 inches, first calculate the z score using the given mean and standard deviation. Then, use the pnorm function in R to find the cumulative probability based on the calculated z score.

Explanation:

In this case, to find the probability that a given rose stem will be shorter than 16.7 inches, you want to calculate the z score first and then find the corresponding probability. The z score formula is:

Z = (X - μ) / σ

where X is the length you're interested in (16.7 inches), μ is the mean length (19.31 inches), and σ is the standard deviation (3.02 inches). So, plug in your values:

Z = (16.7 - 19.31) / 3.02 = -0.8636 approximated

You would then use the R language to find the corresponding probability by using the pnorm function which calculates the cumulative density function (CDF) for a normal distribution. Here's how you would use it:

pnorm(-0.8636)

This will yield value is the probability that the length of a rose stem chosen at random will be less than 16.7 inches.

Learn more about Probability here:

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