X is a normally distributed variable with mean =30 and standard deviation =4.find
a) p(x <40 )
b) p(x> 20)
To find the probabilities, we need to use the standard normal distribution table or a calculator.
a) To find p(x < 40), we need to calculate the z-score first. The z-score formula is z = (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
z = (40 - 30)/4 = 2.5
Looking up the z-score of 2.5 in the standard normal distribution table, we find that the corresponding probability is 0.9938.
Therefore, p(x < 40) = 0.9938.
b) To find p(x > 20), we again need to calculate the z-score:
z = (20 - 30)/4 = -2.5
Looking up the z-score of -2.5 in the standard normal distribution table, we find that the corresponding probability is 0.0062.
However, we want the probability of x > 20, which is the probability of x being greater than 20, so we need to subtract this probability from 1:
p(x > 20) = 1 - 0.0062 = 0.9938.
Therefore, p(x > 20) = 0.9938.