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Answer :
Final answer:
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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