Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance, 24.3% of visitors entered through the Fall River park entrance, 6.3% of visitors entered through the Grand Lake park entrance, and 22.7% of visitors had no recorded point of entry to the park (U.S. National Park Service website). Consider a random sample of 175 Rocky Mountain National Park visitors. Use the normal approximation of the binomial distribution to answer the following questions. 

a. What is the probability that at least 75 visitors had a recorded entry through the Beaver Meadows park entrance? 

b. What is the probability that at least 70 but less than 80 visitors had a recorded entry through the Beaver Meadows park entrance? 

c. What is the probability that fewer than 10 visitors had a recorded entry through the Grand Lake park entrance? 

d. What is the probability that more than 45 visitors have no recorded point of entry?