Question

QUESTION 10 4 If Z is a standard normal random variable, then P(-1.25<= Z <=-0.75) is QUESTION 11 4F It is given that x, the unsupported stem diameter of a sunflower plant, is normally distributed with population mean mu=35 and population standard deviation sigma=3. What is the probability that a sunflower plant will have a basal diameter of more than 40 mm? 4 pc QUESTION 12 A random variable x is normally distributed with u = 100 and o-20, What is the median of this distribution?

Answer 1

Q10) The probability here is computed as:
P(-1.25 <= Z <= -0.75)

= P(Z <= -0.75) - P(Z <= -1.25)

Getting it from the standard normal tables, we have here:
= 0.2266 - 0.1056

= 0.1210

Therefore 0.1210 is the required probability here.

Q11) The distribution here is given as:

$X \sim N(\mu = 35, \sigma = 3)$

The probability here is computed as:
P(X > 40)

$P(Z > \frac{40 - 35}{3})$

$P(Z > \frac{5}{3})$

Getting it from the standard normal tables, we have here:

$P(Z > \frac{5}{3})= 0.0478$

Therefore 0.0478 is the required probability here.

Q12) We are given the distribution here as:

$X \sim N(\mu = 100, \sigma = 20)$

For a normal distribution, median = mean = 100

Therefore 100 is the required median value here.