Question

The height of Maltese dandelions has shown to be a normally distributed random variable; the mean height is 5.7 inches, with a standard deviation of 0.4 inches.i) If you selected a random sample of Maltese dandelions, what % of the plants would you expect to be between 5.3 and 6.1 inches tall?ii) Explain your answer to the previous question.iii) In a random sample of Maltese dandelions, 99.7% of the plants will be between _____ and _____ inches tall.iv) Explain your answer to the previous question.v) In your own words, explain the idea of the normal distribution as it relates to mean and standard deviation.

Answer 1

Given:

Mean= 5.7.

Standard deviation= 0.4

For the normal distribution,

`\begin{gathered} z=(x-\mu)/(\sigma) \\ \mu=5.7,\sigma=0.4 \end{gathered}`

i) The probability that the plants would you expect to be between 5.3 and 6.1 inches tall is,

[tex]\begin{gathered} P(5.3Answer: probability is 0.68268.