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

Question

12 days ago

7

is tested. What is the probability that the sample mean will be less than 295?

2 answers:

tester [12.3K] · Answer 1 · 2026-04-07T14:35:44+03:00

Response:

p = 45.62%

Step-by-step breakdown:

Provided details

μ = 300

σ = 45

X = 295

What is p (X < 295) =?

Applying normal distribution yields:

Z = (X - μ) / σ

⇒ Z = (295 - 300) / 45 = - 0.11

Referring to the table with Z = - 0.11 gives

p (X < 295) = p (Z < -0.11) = 0.4562

Thus, p = 0.4562*100 = 45.62%

AnnZ [12.3K] · Answer 2 · 2026-04-07T14:37:29+03:00

3 0

Response:

$P(\bar{x}$

Step-by-step breakdown:

Average lifespan of electric bulbs = 300 hours

standard deviation = 45

Total tested bulbs = 100

What is the probability that the sample mean is below 295?

Utilizing the Central Limit Theorem

$P(\bar{x}$

Referencing the normal distribution table:

$P(\bar{x}$