Answer:
a) 0.3085
b) 2574
c) 0.0125
Step-by-step explanation:
mean (μ) = 2600 kcal/day and a standard deviation (σ) = 50 kcal/day
a) The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{x-\mu}{\sigma}=\frac{2650-2600}{50}=1[/tex]
From the normal distribution table, P(x > 2650) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587
b) A probability of 30% corresponds with a z score of -0.52
[tex]z=\frac{x-\mu}{\sigma}\\-0.52=\frac{x-2600}{50} \\x-2600=-26\\x=2600-26\\x=2574[/tex]
c) For a sampling distribution of sample mean, the standard deviation is [tex]\frac{\sigma}{\sqrt{n} }[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]
n = 20
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}=\frac{2625-2600}{\frac{50}{\sqrt{20} }}=2.24[/tex]
From the normal distribution table, P(x > 2625) = P(z > 2.24) = 1 - P(z < 2.24) = 1 - 0.9875 = 0.0125
