## Answers

Mean = = 41

Standard deviation = = 8.2

a)

We have given P(X < x) = 0.90

z value 0.90 is 1.28

We have to find the value of x

b)

We have to find P(39 < X < 42)

For finding this probability we have to find a z score.

That is we have to find P( - 0.24 < Z < 0.12)

P( - 0.24 < Z < 0.12) = P(Z < 0.12) - P(Z < - 0.24) = 0.5485 - 0.4037 = **0.1449**

( From z table)

c)

We have to find P(X > 45)

For finding this probability we have to find z score.

That is we have to find P(Z > 0.49)

P(Z > 0.49) = 1 - P(Z < 0.49) = 1 - 0.6872 = **0.3128**

( From z table)

d)

If the probability that pecan tree to have a height greater than 45 feet is less than 0.05 we say that it is unusual.

But P(X > 45) = 0.3128 > 0.05 so it is not unusual.

e)

Sample size = n = 36

We have to find P( > 45)

For finding this probability we have to find z score.

That is we have to find P(Z > 2.93)

P(Z > 2.93) = 1 - P(Z < 2.93) = 1 - 0.9983 = **0.0017**

( From z table)

f)

If the probability that mean height pecan tree 45 feet is less than 0.05 we say that it is unusual.

In this case P( > 45) = 0.0.0017 < 0.05 so it is unusual.