Question

normal curve that corresponds to the required area.

Jose who lives in Zambales harvested mangoes in her plantation for

export. The average weight of the harvested fruits is 2 kilos with a

standard deviation of 0.4 kilo. Assume that the variable is normally

distributed.

a. What is the probability that a randomly selected mango will weigh less

than 1.5 kilos?

_____________________________________________________________________

_____________________________________________________________________

b. A potential importer intends to take a sample of 4 mangoes and will not

place an order if the sample mean is less than 1.5 kilos. What is the

probability that the importer will not place an order?

Answer 1

Solution

Mean $\mu =2.0$

Standard deviation $\sigma=0.4$

(a) Probability that a randomly selected mango weighs less than 1.5 Kg

$X=1.5$

$Z=\dfrac{X-\mu}{\sigma}$

$Z=\dfrac{1.5-2.0}{0.4}=-1.25$

From normal distribution tables

Probability of Z(-1.25)

$=0.10565$

(b) Probability that an importer will not place an order

$=\dfrac{\sigma}{\sqrt{\smash[b]{n}}}=\dfrac{0 .4}{\sqrt{\smash[b]{4}}}=0.2$

$Z=\dfrac{1.5-2.0}{0.2}=-2.5$

From normal distribution tables

Probability $=0.0062$