Question

A botanist is collecting data from a particular species of plant. The scientist found that the data is normally distributed with a mean value of =147 μ = 147 cm and standard deviation of =30 σ = 30 cm. If the sample size is =4000 N = 4000 how many specimens have a height greater than 73 73 cm

Answer 1

Answer:

3972.72 specimens

Step-by-step explanation:

We solve using the z score formula:

z = (x-μ)/σ where

x is the raw score = 73 cm

μ is the population mean = 147 cm

σ is the population standard deviation = 30 cm

N is the number of samples = 4000

For x > 73

z = 73 - 147/30

z = -2.46667

Probability value from Z-Table:

P(x<73) = 0.0068189

P(x>73) = 1 - P(x<73) = 0.99318

The probability of having a height greater than 73cm is: 0.99318

The number of specimens that have a height greater than 73cm is calculated as: 0.99318 × 4000

= 3972.72 specimens