Question

3. The heights of certain plants are normally distributed with a mean of 6.84 cm. It is known that the shortest 12.5% are below 5.91 cm. a) Write down the standardized score (z-score) of 5.91 cm. b) Hence, find the standard deviation of the heights of the plants. c) A plant is selected at random. Find the probability that i) the plant is taller than 7 cm. ii) the plant is between 5 and 8 cm. iii) the plant is shorter than 4 cm.

          3. The heights of certain plants are normally distributed with a mean of 6.84 cm. It is known that the shortest 12.5% are below 5.91 cm.

a) Write down the standardized score (z-score) of 5.91 cm.
b) Hence, find the standard deviation of the heights of the plants.
c) A plant is selected at random. Find the probability that
i) the plant is taller than 7 cm.
ii) the plant is between 5 and 8 cm.
iii) the plant is shorter than 4 cm.

3. The heights of certain plants are normally distributed with a mean of 6.84 cm. It is known that the shortest 12.5% are below 5.91 cm.

a) Write down the standardized score (z-score) of 5.91 cm.
b) Hence, find the standard deviation of the heights of the plants.
c) A plant is selected at random. Find the probability that
i) the plant is taller than 7 cm.
ii) the plant is between 5 and 8 cm.
iii) the plant is shorter than 4 cm.

Added by Ricardo W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/07/2023

Step 1

91 cm), μ is the mean (6.84 cm), and σ is the standard deviation. We know that the shortest 12.5% of plants are below 5.91 cm, so we can find the z-score corresponding to the 12.5th percentile using a z-table or calculator. The z-score for the 12.5th percentile is Show more…

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The heights of certain plants are normally distributed with a mean of 6.84 cm. It is known that the shortest 12.5% are below 5.91 cm. a) Write down the standardized score (z-score) of 5.91 cm. b) Hence, find the standard deviation of the heights of the plants. c) A plant is selected at random. Find the probability that i) the plant is taller than 7 cm ii) the plant is between 5 and 8 cm iii) the plant is shorter than 4 cm.