Question

According twhat amourThe graph shows the distribution of the amount ofchicken (in ounces) that adults eat in one sitting. Thedistribution is approximately Normal, with a mean of 8ounces and a standard deviation of 1.2 ounces.O 4.4 ounc不O 5.6 ouncChicken Consumption0 10.4 oundO 11.6 ounc

Answer 1

To answer this question, we can proceed as follows:

1. We have a normal distribution with a mean, μ = 8 ounces, and a standard deviation, σ = 1.2 ounces.

2. We need to determine the value, x, in the distribution for which the cumulative probability is less than 2.5%.

3. To do this, we can use the z-scores, and they are defined as:

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

And we already know that:

• μ = 8 ounces

,

• σ = 1.2 ounces

4. If we consult the cumulative standard normal distribution table, we need to find the corresponding value for z for a cumulative probability of 2.5%. Then we have:

$P(z<-1.96)=0.025$

Therefore, we have the corresponding value of z for a cumulative probability of 2.5% (=2.5/100) is z = -1.96.

5. Now, to find the value of x, we can proceed as follows:

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ -1.96=\frac{x-8}{1.2} \end{gathered}$

6. Multiply both sides of the equation by 1.2:

$(1.2)(-1.96)=x-8$

7. And now add 8 to both sides of the equation:

$\begin{gathered} (1.2)(-1.96)+8=x \\ \\ \\ x=(1.2)(-1.96)+8 \\ x=5.648 \end{gathered}$

If we round the result to the nearest tenth, we have x = 5.6 ounces.

And we can see that in the following graph:

Therefore, according to the graph, 2.5% of adults eat less than 5.6 ounces of chicken in one sitting (second option).