Respuesta :
Answer:
The latest 2.5% of bills will be received in 20 more days after mail-out.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 31 days
Standard Deviation, σ = 6 days
We are given that the distribution of The number of days (X) is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]P(X \leq x) = 0.025[/tex]
We have to find the value of x such that the probability is 0.025
[tex]P(X \leq x) = 0.025[/tex]
[tex]P( X \leq x) = P( z \leq \displaystyle\frac{x - 31}{6})=0.025[/tex]
Calculation the value from standard normal z table, we have,
[tex]P( z \leq -1.960) = 0.025[/tex]
[tex]\displaystyle\frac{x - 31}{6} = -1.960\\x = 19.24 \approx 20[/tex]
Hence, the latest 2.5% of bills will be received in 20 more days after mail-out.
