Question

A certain brand of electric bulbs has an average life of 300 hours with a standard deviation of 45. A random sample of 100 bulbs is tested. What is the probability that the sample mean will be less than 295?

Answer 1

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%

Answer 2

Answer:

$P(\bar{x}$

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

$P(\bar{x}$

From table of normal distribution:

$P(\bar{x}$