A new lightbulb has been developed with a mean lifetime of 1800 hours and standard deviation of 100 hours. A sample of 100 of these bulbs is tested. The sample mean lifetime is 1770 hours. (a) What is the probability of obtaining a sample mean that is less than or equal to 1770 hours? (5 points) (b) Would it be unusual to obtain a sample mean of less than or equal to 1770 hours? (5 pts

a) The probability of obtaining a sample mean that is less than or equal to 1770 hours is P(M≤1770)=0.0013.

b) It is unusual, as there are only 13 chances in 10,000 (0.13%) of having this outcome.

Step-by-step explanation:

We have a population lifetime with mean of 1800 hours and standard deviation of 100 hours.

Samples of size n=100 are taken and tested.

We can calculate the probability of obtaining a sample mean that is less than or equal to 1770 hours using a z-score for the sample Mean M=1770 and then calculating its probability according to the standard normal distribution:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

won't that be plagrisim thought?

step-by-step explanation: