Answer:
[tex]P(\bar{x}<295)=0.4207[/tex]
Step-by-step explanation:
Average life of electric bulbs = 300 hrs
standard deviation = 45
Total no of bulbs tested = 100
Probability that sample mean is less than 295 =?
Using Central Limit Theorem
[tex]P(\bar{x}<295)=P(Z<\frac{x-\mu}{\sigma})\\P(Z<(-0.2)\approx \phi(-0.2)[/tex]
From table of normal distribution:
[tex]P(\bar{x}<295)=0.4207[/tex]
Answer:
p = 45.62%
Step-by-step explanation:
Given
μ = 300
σ = 45
X = 295
p (X < 295) = ?
We can apply the Normal Distribution as follows
Z = (X - μ) / σ
⇒ Z = (295 - 300) / 45 = - 0.11
using the table with Z = - 0.11 we have
p (X < 295) = p (Z < -0.11) = 0.4562
⇒ p = 0.4562*100 = 45.62%
