The town of Willoughby has just been selected as the site for a new automobile assembly complex. City officials estimate that the anticipated influx of job-seeking families will add some four hundred students to Willoughby’s public high schools.
(a) What family of random variables is the number 400 likely to represent, and what is its standard deviation? Explain.
(b) Every new high school student in Willoughby is given a diagnostic test whose scores tend to be normally distributed with a mean (μ) of 200 and a standard deviation (σ) of 40. Any student scoring below 120 is provided with remedial instruction, and those scoring above 290 are offered additional honors courses. What is the probability that a new student qualifies for special instruction?
(c) Every student requiring special instruction costs the city an additional $1500.00. Suppose four hundred new high school students do, in fact, enroll next Fall. The Willoughby School Board has budgeted $20,400.00 to cover the cost of providing whatever additional instruction they might need. Is that amount likely to be sufficient? Explain.