Q10 - investigate

A nutritionist who investigates fruits reported that the average weight of a raspberry is 4.4 g with a standard deviation of 1.28 g. What is the probability that a randomly selected raspberry would weigh less than 3.1 grams?

Let X represent the weight of a randomly selected raspberry. Assume the distribution of weights is approximately normal. Find P( X < 3.1).

Round your answer to two decimal places.

Correct answer:

p =  0.16

Step-by-step explanation:

$$\begin{gathered} m=4.4\text{g} \\ \sigma =1.28\text{g} \\ p=P(x<3.1g) \\ {m}_1=m-\sigma =4.4-1.28=\frac{78}{25}=3\frac{3}{25}=3.12\text{g} \\ {m}_2=m-2\cdot \sigma =4.4-2\cdot 1.28=\frac{46}{25}=1\frac{21}{25}=1.84\text{g} \\ {m}_3=m-3\cdot \sigma =4.4-3\cdot 1.28=\frac{14}{25}=0.56\text{g} \\ p=\frac{1-0.6827}{2}=0.16 \end{gathered}$$

Use the normal distribution table.

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