Chapter 2.2, Problem 55E

To determine

Percentage of the meals ordered exceeded the recommended daily allowance of 2400 mg of sodium.

Answer to Problem 55E

Around 21.19% of the meals ordered exceeded the recommended daily allowance of 2400 mg of sodium.

Explanation of Solution

Given information:

Daily allowance, $x=2400\text{mg}$

Mean, $\mu =2000\text{mg}$

Standard deviation, $\sigma =500\text{mg}$

Calculations:

Calculate the Z − score,

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

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with 0.8 and the column that starts with .00 of the standard normal probability table for $P\left(z<0.80\right)$ .

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

Therefore,

Around 21.19% of the meals ordered exceeded the recommended daily allowance of 2400 mg of sodium.