Answer to Question #309258 in Statistics and Probability for kate

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?

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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 $=0.0062$