A set of data items is normally distributed with a mean of 50 and a standard deviation of 4 . Convert 40 to a z-score. \( z_{40}=\square \) (Type an integer or a decimal.)

To convert a value into a z-score, you use the formula: \( z = \frac{(X - \mu)}{\sigma} \), where \( X \) is the value you're converting, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Here, \( X = 40 \), \( \mu = 50 \), and \( \sigma = 4 \). So, substituting the values in gives you: \( z_{40} = \frac{(40 - 50)}{4} = \frac{-10}{4} = -2.5 \). Therefore, \( z_{40} = -2.5 \). Get ready to impress your friends with how easily you tackle statistics! Just remember, normal distribution isn’t just a textbook concept; it's a handy tool in everything from predicting outcomes in sports to making stock market investments! Understanding how z-scores work can help you assess probabilities and make data-informed decisions in real life. Also, keep an eye out for common errors! A frequent mistake is confusing the z-score's interpretation. A z-score tells you how many standard deviations a point is from the mean but doesn't indicate the value itself—so don't mix those up! Keep practicing, and you'll soon be z-scaling like a pro!