Question

Libraries in North Dakota receive funding based on the number of people who join the library. To determine the number of people who joined the library, one library day is selected at random and the number of people who joined that day is counted and used for funding purposes. The daily number of no registration is approximately normally distributed with mean 120 students and standard deviation 10.5 students.

(a) If more than 140 people are not joining on the day the registration count is taken for funding purposes, the North Dakota library will lose some of its state funding in the subsequent year. Approximately what is the probability that the library will lose some of its funding? Show your work and label your answer with appropriate probability notation.

(b) The library association in North Dakota suggests that instead of choosing one day at random, the state should choose 3 days at random. With the suggested plan, The particular library would lose some of its state funding in the subsequent year if the mean number of people not joining for the 3 days is greater than 140. Approximately what is the probability that the library would lose funding using this suggested plan? Show your work and label your answer with appropriate probability notation.

Would Dakota public library be more likely, less likely, or equally likely to lose funding using the plan suggested by the Library association described in part (b) compared to the plan described in part (a)? Explain.

Answer 1

The daily number of no registration is approximately normally distributed with

a) the probability that the library will lose some of its funding is if more than 140 people are not joining on the day the registration count is taken for funding purposes =

b) the probability that the library would lose funding using this suggested plan =

Dakota public library be more likely to lose funding using the plan suggested by the Library association described in part (b) compared to the plan described in part because of the standard error gets reduced and the effect size is large enough for small sample to detect.