Long Questions (Question 6)

Posted on May 17, 2020 by Myhometuition

Question 6:

The masses of tomatoes in a farm are normally distributed with a mean of 130 g and standard deviation of 16 g. Tomato with weight more than 150 g is classified as grade ‘A’.

(a) A tomato is chosen at random from the farm. Find the probability that the tomato has a weight between 114 g and 150 g.

(b) It is found that 132 tomatoes in this farm are grade ‘A’. Find the total number of tomatoes in the farm.

Solution:

µ = 130

σ = 16

(a)

\begin{array}{l} P (114 < X < 150) \\ = P (\frac{114 - 130}{16} < Z < \frac{150 - 130}{16}) \\ = P (- 1 < Z < 1.25) \\ = 1 - P (Z > 1) - P (Z > 1.25) \\ = 1 - 0.1587 - 0.1056 \\ = 0.7357 \end{array}

(b)

Probability of getting grade ‘A’ tomatoes,

P (X > 150) = P (Z > 1.25)

= 0.1056

\begin{array}{l} Lets total number of tomatoes = N \\ 0.1056 \times N = 132 \\ N = \frac{132}{0.1056} \\ N = 1250 \end{array}