Question

(100 POINTS) The weights of boxes of rice noodles produced at a factory are normally distributed with a mean of 38 ounces and a standard deviation of 1.7 ounces. Consider a shipment of 3500 boxes of rice noodles.

How many of the boxes will weigh 37.5 ounces or less?
A: 974
B: 1345
C: 2526
D: 3114

Answer 1

B) 1,345

Explanation:

To find out how many boxes will weigh 37.5 ounces or less, find the probability that a random box of rice noodles weighs 37.5 ounces or less then multiply it by the number of boxes in the shipment.

The weights of boxes of rice noodles produced at a factory are normally distributed with a mean (μ) of 38 ounces and a standard deviation (σ) of 1.7 ounces. Therefore:

`\rm X \sim N(\mu,\sigma^2)\implies \boxed{\rm X \sim N(38,1.7^2)}`

where X is the weight of the rice noodles boxes in ounces.

To calculate the probability that a random box of rice noodles weighs 37.5 ounces or less, we need to find P(X ≤ 37.5).

Calculator input for "normal cumulative distribution function (cdf)":

• Upper bound: x = 37.5
• Lower bound: x = -1000
• μ = 38
• σ = 1.7

This gives the probability that a random box of rice noodles weighs 37.5 ounces or less as:

`\rm P(X\leq 37.5) = 0.384334003...`

Multiply the found probability by the number of boxes in the shipment:

`\begin{aligned}\sf Number\;of\;boxes&=\sf Probability * Total\;boxes\\&=0.384334003... * 3500 \\&= 1345.16901...\\&=1345\; \sf boxes\end{aligned}`

Therefore, approximately 1,345 boxes of rice noodles in a shipment of 3,500 boxes will weight 37.5 ounces or less.