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german
1 year ago
7

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?
Mathematics
2 answers:
GarryVolchara [31]1 year ago
5 0

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%

tigry1 [53]1 year ago
3 0

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}

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