Statistics- THank you

Question

A random number generator picks a number from 5 to 58 in a uniform manner. Round answers to 4 decimal places when possible.

1. The mean of this distribution is Correct
2. The standard deviation is Correct
3. The probability that the number will be exactly 39 is P(x = 39) = Correct
4. The probability that the number will be between 18 and 46 is P(18 < x < 46) = 
5. The probability that the number will be larger than 18 is P(x > 18) = 
6. P(x > 19 | x < 56) = 
7. Find the 18th percentile. 
8. Find the minimum for the upper quartile. 

Answer 1

This is a uniform distribution ~ U(5, 58). I'll assume it is continuous since it mentions 4 decimal places.

1. The mean is the average of a and b where U(a, b). So, it is (5+58)/2 = 31.5
2. The standard deviation is given by ((b-a)^2)/12 = ((58-5)^2)/12= 234.0833
3. Use the pdf. P(x=39) = f(39) = 1/(b-a) = 1/(58-5) = 0.0189
4. You would need the cdf here F(x) = (x-a)/(b-a) = (x-5)/53. P(18 < x < 46) = P(x < 46) - P(x < 18) = ((46-5)/53) - ((18-5)/53) = 0.5283
5. Using what we know from 4. above, we have, P(x > 18) = 1 - P(x < 18) = 1 - ((18-5)/53) = 0.7547
6. P(x < 19 | x < 56) = P(x < 19 AND x < 56) / P(x < 56) = P(x < 19)/P(x < 56) = ((19-5)/53)/((56-5)/53) = 0.2745
7. We need to find the y such that P(x < y) = 0.18. So, F(y) = (y-5)/53 = 0.18. So, y = 14.72.
8. Similar to 7. above, P(x < z) = 75. So, F(z) = (z-5)/53 = 0.75. So, z = 44.75.

Hope this helps!