Answer:
P10 = 27.4
P90 = 22.0
It helps the producer to know the higher (P10) and lower estimates (P90) for the amount of chocolate chips per cookie.
Step-by-step explanation:
In P10 and P90 the P stands for "percentile".
In the case of P10, indicates the value X of the random variable for which 10% of the observed values will be above this value X.
In the case of P90, this percentage is 90%.
In this case, we can calculate from the z-values for each of the percentiles in the standard normal distribution.
For P10 we have:
[tex]P(z>z_{P10})=0.1\\\\z_{P10}=1.2816[/tex]
For P90 we have:
[tex]P(z>z_{P90})=0.9\\\\z_{P90}=-1.2816[/tex]
Then, we can convert this values to our normal distribution as:
[tex]P10=\mu+z\cdot\sigma=24.7+1.2816\cdot 2.1=24.7+2.7=27.4 \\\\P90=\mu+z\cdot\sigma=24.7-1.2816\cdot 2.1=24.7-2.7=22.0[/tex]
