Please help me I've been waiting all day for help on these statistics problems :/?

Question

If you can only answer one, that's completely fine. I've been waiting for a long time for help on these so thank you for looking at this <3

1) In a random sample of 30 tires of the same type, it is found that the average life span of a tire is 36,200 miles with a standard deviation of 3,800 miles. Find the probability that the mean of the population will be less than 560 miles from the mean of the sample.

A) 80.7%
B) 57.6%
C) 1.3%
D) 8.1%

2) The table looks like this:

Amount Frequency
0-8-----------------18
8-16----------------15
16-24---------------16
24-32---------------11
32-40---------------9
40-48---------------6

The question is: Estimate the median of the table.

A) 19
B) 16
C) 20
D) 18

3) A set of 300 values has a normal distribution with a mean of 50 and a standard deviation of 5. Find the probability that a value selected at random from this data is between 49.5 and 50.5

Answer 1

1) For this problem, we need to start by finding the standard error of the mean for the sample.

(standard error) = (standard deviation) / sqrt(n)

where n is the sample size. So in this case,

(standard error) = 3800 / sqrt(30)
................ = 693.8 mi

This means that if we took a whole bunch of different samples of 30 tires each and calculated the mean lifespan of each sample, the standard deviation of all these means would be 693.8 mi.

Now that we have this value, we can compute the z-score associated with a deviation of 560.

z = 560 / 693.8 = 0.807

So what we want is the probability that a point under the normal distribution is between z=-0.807 and z=+0.807. We need to look this up in a z table, or use a calculator. I use the app

http://davidmlane.com/hyperstat/z_table....

and I found the probability was 58.03%. I'm guessing B) is the right answer.

2) The median value is the value in the middle of a list of values. That is, there are as many values above the median value as there are below the median value.

Adding up all the numbers in the frequency column gives 75, so there are 75 values in this list total. That means the 38th value in the list is the median (there are 37 values lower than it and 37 values higher). The 38th value in the list is the 5th value in the category 16-24 (there are 18 values in the 0-8 range, 15 in the 8-16 range, and the first 4 values in the 16-24 range that are all lower: 18+15+4=37). This is very tough to guess, since we don't have any idea how the values are distributed in the 16-24 region. I would guess that the value is 19, but it could really easily be 18 or 20. So my best guess is A), but I really think that the question is too vague to be answered accurately.


3) If you have a calculator that does statistical calculations, this could be very easy. Usually there is a normal distribution function, and you would put the values

mean = 50
standard deviation = 5
lower bound = 49.5
upper bound = 50.5

and just calculate the probability.

If you don't have such a calculator, you can still find the result by converting to a z-score.

z = (x - mean) / (standard deviation)

So z for the lower bound is

z = (49.5 - 50) / 5 = -0.1

and z for the uppoer bound is

z = (50.5 - 50) / 5 = +0.1

So we need to find the probability that a point in the normal distribution is between z = -0.1 and z = +0.1. Using a table or calculator gives the probability as 8.0%

source: https://answers.yahoo.com