Respuesta :
Answer:
a) 0.013
b) 0.7
c) 0.866
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 1262
Standard Deviation, σ = 118
We are given that the distribution of number of chocolate chips is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(fewer than 1000 chocolate chips)
P(x < 1000)
[tex]P( x < 1000) = P( z < \displaystyle\frac{1000 - 1262}{118}) = P(z < -2.220)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 1000) = 0.013 = 1.3\%[/tex]
b) P(contains more than 1200 chocolate chips)
[tex]P(x > 1200) = P(z > \displaystyle\frac{1200-1262}{118}) = P(z > -0.5254)\\\\P( z > -0.5254) = 1 - P(z \leq -0.5254)[/tex]
Calculating the value from the standard normal table we have,
[tex]1 - 0.300 = 0.7 = 70\%\\P( x > 1200) = 0.7[/tex]
c)P(contains between 1000 and 1400 chocolate chips)
[tex]P(1000 \leq x \leq 1400) = P(\displaystyle\frac{1000 - 1262}{118} \leq z \leq \displaystyle\frac{1400-1262}{118}) = P(-2.22 \leq z \leq 1.169)\\\\= P(z \leq 1.169) - P(z < -2.22)\\= 0.879 - 0.013 = 0.866 = 86.6\%[/tex]
[tex]P(1000 \leq x \leq 1400) = 86.6\%[/tex]
