QUESTION TWO Rawiri's father works as a quality control manager at a food packaging and processing plant. He knows from experience that the packed weights of the Ruffles brand of potato chips, which they produce, are normally distributed with mean 155 g and standard deviation $$ 2 \mathrm{~g} \cdot $$ The labelling on each of the packets of potato chips states a minimum contents of 150 g . (a) Find the probability that a randomly selected packet of Ruffles potato chips weighs: (i) between 157 g and 160 g .

Question

UpStudy AI · Accepted Answer

To find the probability that a randomly selected packet of Ruffles potato chips weighs between 157 g and 160 g, we can use the properties of the normal distribution.

Given:
- Mean ($$\mu$$) = 155 g
- Standard deviation ($$\sigma$$) = 2 g

We need to find the probability $$P(157 < X < 160)$$, where $$X$$ is the weight of the potato chips.

First, we will standardize the values using the z-score formula:

$$
z = \frac{X - \mu}{\sigma}
$$

1. **Calculate the z-scores for 157 g and 160 g:**

For $$X = 157$$:
   $$
   z_{157} = \frac{157 - 155}{2} = \frac{2}{2} = 1
   $$

For $$X = 160$$:
   $$
   z_{160} = \frac{160 - 155}{2} = \frac{5}{2} = 2.5
   $$

2. **Find the probabilities corresponding to these z-scores using the standard normal distribution table (or a calculator):**

- $$P(Z < 1)$$ corresponds to $$z = 1$$.
   - $$P(Z < 2.5)$$ corresponds to $$z = 2.5$$.

Using a standard normal distribution table or calculator:
- $$P(Z < 1) \approx 0.8413$$
- $$P(Z < 2.5) \approx 0.9938$$

3. **Calculate the probability that $$X$$ is between 157 g and 160 g:**

$$
P(157 < X < 160) = P(Z < 2.5) - P(Z < 1)
$$
$$
P(157 < X < 160) = 0.9938 - 0.8413 = 0.1525
$$

Thus, the probability that a randomly selected packet of Ruffles potato chips weighs between 157 g and 160 g is approximately **0.1525** or **15.25%**.
The probability that a randomly selected packet of Ruffles potato chips weighs between 157 g and 160 g is approximately 0.1525 or 15.25%.

Real Tutor Solution

Answer

Solution

Related Questions

Latest Statistics Questions