a tomatoe plant population has a height, which are normally distributed with a mean of 80 cm and a standard deviation of 5 cm. what is the proportion of plant w

Question

a tomatoe plant population has a height, which are normally distributed with a mean of 80 cm and a standard deviation of 5 cm. what is the proportion of plant with heights:
less than 72cm?
Between 82cm and 87 cm?
Between 72cm and 82 cm?

Answer 1

You need to use the Standard Normal Distribution table for the various z scores.

 

For < 72 cm, the z score is -2; the table gives area under curve up to that point as 0.02275, which means only 2.275% of the TOMATO plants afre under 72 cm high.

 

For the second part,the z scores are z₈₂ = 0.4 and z₈₇ = 1.4 so the respective areas are 0.65542 and 0.91934 which gives net area under curve 0.26382, meaning that 26.382 of the TOMATO plants have heights between 82 cm & 87 cm.

 

Get it?