Answer:
The probability that X is between 38 and 76 is 0.68268.
Step-by-step explanation:
We are given that X is a normally distributed random variable with mean 57 and standard deviation 19.
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 57
= standard deviation = 19
Now, the probability that X is between 38 and 76 is given by = P(38 < X < 76)
P(38 < X < 76) = P(X < 76) - P(X 38)
P(X < 76) = P( < ) = P(Z < 1) = 0.84134
P(X 38) = P( ) = P(Z -1) = 1 - P(Z < 1)
= 1 - 0.84134 = 0.15866
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.84134.
Therefore, P(38 < X < 76) = 0.84134 - 0.15866 = 0.68268.