Question

Note: Use SPSS to solve the following questions. For every question Write the SPSS command and then copy and paste the output page here (or in some cases the screenshot of the data view that shows the output).

Can I Know also what is the sample file (in SPSS) that we work on?

Question : (In this problem first find the probability by using SPSS and then calculate the number of trees manually by using the probabilities.)

A certain variety of pine tree has a mean trunk diameter of μ= 150 cm, and a standard deviation of σ= 30 cm which is normally distributed. A certain section of a forest has 500 of these trees. Find Approximately

1. how many of these trees have a diameter smaller than 120

2. how many of these trees have a diameter greater than 160

3. how many of these trees have a diameter between 130 and 160.

4. how many of these trees have a diameter between 120 and 140.

Answer 1

Solution :

Given that ,

mean = = 150

standard deviation = =30

1) P(x < 120) = P[(x - ) / < (120-150) /30 ]

= P(z <-1 )

= 0.1587

probability =0.1587*500 = 79 trees

Answer = 79 trees

2)

P(x >160 ) = 1 - p( x<160 )

=1- p [(x - ) / < (160-150) /30 ]

=1- P(z < 0.33)

= 1 - 0.6293 = 0.3707

probability = 0.3707*500 = 185

Answer = 185 trees

c)

P( 130< x < 160 ) = P[(130-150 )/30 ) < (x - ) /  < (160-150 ) /30 ) ]

= P( -0.67< z <0.33 )

= P(z <0.33 ) - P(z < -0.67)

Using standard normal table

= 0.6293- 0.2514 = 0.3779

Probability = 0.3779*500 = 189 trees

Answer = 189 trees

d)

P( 120< x < 140 ) = P[(120-150 )/30 ) < (x - ) /  < (140-150 ) /30 ) ]

= P( -1 < z < -0.33 )

= P(z < -0.33 ) - P(z < -1)

Using standard normal table

= 0.3707 - 0.1587 = 0.212

Probability = 0.2120*500 = 106 trees

Answer = 106 trees