A student reported that46% of college students aged18-24 would spend their winter break at home in 2021. A sample of145 college students was selected.

Calculate the standard error of the proportion

What is the probability that less than 40% of the college students from the sample spent their winter break at home?

P(less than 40%) of the college students from the sample spent their winter break at home)=

What is the probability that more than 50% of the college students from the sample spent their winter breaks at home?

P(less than 50%) of the college students from the sample spent their winter break at home)=

P(between 49% and 59%) of the college students from the sample spent their winter break at home)=

I really appreciate if the formulas are included as well.

Thanks!