Stats
posted by Ryan .
The distribution of lifetimes for a particular brand of lightbulbs has a mean of 110 hours and a standard deviation of 20 hours. Suppose a random sample of 35 lightbulbs is taken for observation.
What is the probability that the sample mean lifetime will be between 105 and 115 hours?
0.4306
0.3026
0.1974
0.7372
0.8612
What value does the sample mean exceed with 95% probability (Hint: This is the 5th percentile for the sample mean distribution)?
77.10
106.79
104.44
116.63
115.56

For an individual bulb, the probability of a life between 105 and 115 hours is 0.1974. I used a normal probability calculator to get that.
For 35 bulbs, the mean of the average remains 110 but the standard deviation is 20/sqrt35 = 3.38. The probabilty of the mean being between 105 and 115 is then 0.861.
For your second question, I get 104.4