Question

Use the Normal model ​N(​1119,​89) for the weights of steers. ​a) What weight represents the 37th ​percentile? ​b) What weight represents the 97th ​percentile? ​c) What's the IQR of the weights of these​ steers?

Answer 1

To find the weights representing the 37th and 97th percentiles in a normal distribution N(1119, 89), z-scores for these percentiles are required and then converted into actual weights. The Interquartile Range (IQR) is the difference between the 25th and 75th percentile weights.

Step-by-step explanation:

The normal distribution model N(1119, 89) describes the weights of steers with a mean (μ) of 1119 pounds and a standard deviation (σ) of 89 pounds.

• 37th percentile: To find the weight representing the 37th percentile, we need to use the standard normal distribution table or a calculator that provides inverse normal functions. The 37th percentile corresponds to a z-score, which we find and then transform it to the actual weight using the equation X = μ + zσ.
• 97th percentile: Similarly, to find the weight representing the 97th percentile, we follow the same process as for the 37th percentile using the 97th percentile's specific z-score.
• Interquartile range (IQR): The IQR is the range between the first quartile (25th percentile) and the third quartile (75th percentile). Again, we find the z-scores corresponding to these percentiles and then transform them into actual weights using the distribution's parameters to determine the IQR.