A survey of recent first-time home buyers found that 45% of them plan to upgrade to a bigger house within 5 years. You randomly select 30 recent first-time home buyers and ask them whether they plan to upgrade to a bigger home within 5 years.
Use the normal approximation and the mean and standard deviation you found above to find the probability that more than 20 of the recent first-time home buyers plan to upgrade to a bigger home within 5 years. Leave your answer as a decimal with 4 decimal places.