Final answer:
To find the x value c such that P(X < c) = 0.5, we need to calculate the z-score for the given mean and standard deviation. Using the formula z = (x - mean) / standard deviation, we can solve for the x value c. In this case, c = 37.
Step-by-step explanation:
The z-score represents the number of standard deviations a data point is from the mean of a normal distribution. To find the z-score for a given x value, we can use the formula z = (x - mean) / standard deviation. In this case, the mean is 37 and the standard deviation is 4, so the z-score for the x value c can be calculated as z = (c - 37) / 4.
To find the x value c such that P(X < c) = 0.5, we need to find the z-score for which the cumulative probability is 0.5. Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.5 is 0. Therefore, we have the equation (c - 37) / 4 = 0, which can be solved to find c = 37.