Final answer:
The expected value for patients with a severe language barrier is 192.4, calculated by multiplying the sample size of 520 by the expected proportion of 37%.
Step-by-step explanation:
The student is dealing with a concept from statistics called the Goodness of Fit test, which evaluates whether a set of observed category frequencies matches a theoretical expected frequency distribution. To calculate the expected value for those with a severe barrier given a sample of 520 patients, you multiply the total sample (520) by the proportion expected for that category (37%).
Expected value = Total number of patients × Proportion of severe barrier
= 520 × 0.37
= 192.4