Normal Distribution (continued): Fresh Take

  • Understand the properties and characteristics of the standard normal distribution.
  • Calculate probabilities and percentiles using normal distribution and [latex]z[/latex]-scores with technology.

Recall that a normal distribution is a mathematical model with a smooth bell-shaped curve. Let’s look at an example of how to calculate probabilities using normal distribution.

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A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal distribution with a mean diameter of [latex]5.85[/latex] cm and a standard deviation of [latex]0.24[/latex] cm.(a) Find the probability that a randomly selected mandarin orange from this farm has a diameter larger than [latex]6.0[/latex] cm.

(b) The middle 20% of mandarin oranges from this farm have diameters between ______ and ______.

(c) Find the [latex]90[/latex]th percentile for the diameters of mandarin oranges and interpret it in a complete sentence.