Question

Watch the salt! A study investigated about $3000$ meals ordered from

Chipotle restaurants use the online site Grubhub. Researchers calculated the sodium content (in milligrams) for each order based on Chipotle’s published nutrition information. The distribution of sodium content is approximately Normal with a mean of $2000$mg and a standard deviation of $500$mg.$10$About what percent of the meals ordered exceeded the recommended daily allowance of $2400$ mg of sodium?

Short answer

Around $21.19$ percent of the meals ordered included more sodium than the daily limit of $2400$ mg.

Step-by-step solution

Given information

Daily allowance,$x=2400mg$

Mean,$\mu =2000mg$

Standard deviation,$\sigma =500mg$

Concept

The formula used:$z=\frac{x-\mu }{\sigma }$

Calculation

Calculate the $Z-$score,

$z=\frac{x-\mu }{\sigma }=\frac{2400mg-2000mg}{500mg}=0.80$

To find the equivalent probability, use the normal probability table in the appendix.

See the usual normal probability table for $P(z<0.80)$in the row that starts with $0.8$and the column that starts with$.00.$

$$\begin{gathered} P(x>2400)=P(z<0.80) \\ =1-P(z>0.80) \\ =1-0.7881 \\ =0.2119 \\ =21.19\% \end{gathered}$$

Therefore,

Around $21.19$ percent of the meals ordered included more sodium than the daily limit of $2400$ mg.