Question

Jim tree wants to analyze his shipment of trees based on height. he knows the height of the trees is normally distributed so he can use the standard normal distribution. he measures the height of 100 randomly selected in his shipment. he finds the mean is 65 inches and the standard deviation is 10 inches. what percentage of the trees will be between 55 inches and 75 inches? 60% or 34%

Answer 1

The percentage is 68%

Answer 2

100 randomly selected trees were measured. The mean is
`\mu=65` inches and the standard deviation is
`\sigma=10` inches. To find the percentage of the trees that will be between 55 inches and 75 inches, first note that

• 
  `55=65-10=\mu-\sigma;`
• 
  `75=65+10=\mu+\sigma.`

This means that all trees between 55 inches and 75 inches are within one standard deviation. See attached graph to calculate that the percentage of the trees between 55 inches and 75 inches is 68%.

Answer: 68%