A market research firm is studying customer satisfaction for a food delivery service. Based on past data, $85\%$ of customers rate the service as "satisfactory". The firm randomly surveys groups of 250 customers. Find the mean ${\mu }_{\hat{p}}$ and standard deviation ${\sigma }_{\hat{p}}$ of the sampling distribution for $\hat{p}$. What would the shape of the sampling distribution be?

A bank analyzes customer adoption of its new mobile banking app. Historically, 45% of customers use online banking services. Use a normal distribution to approximate the probability that between 62 and 70 customers out of a sample of 100 will adopt the online banking service.

A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that a random sample of $100$ people reveals $60$ people or more preferring Pepsi. 

A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that, from this same random sample of $100$ people, that between $10$ and $11$ people prefer Coca Cola.

A bank analyzes customer adoption of its new mobile banking app. Historically, 45% of customers use online banking services. Use a normal distribution to approximate the probability that between 62 and 70 customers out of a sample of 100 will adopt the online banking service.