The Wall Street Journal reported that the age at first startup for $55\%$ of entrepreneurs was $29$ years of age or less and the age at first startup for $45\%$ of entrepreneurs was $30$ years of age or more.

$($a$)$ Suppose a sample of $200$ entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Calculate the sampling distribution of p where p is the sample proportion of entrepreneurs whose first startup was at $29$ years of age or less. If required, round your answers to four decimal places.

np $=$

n$(1-$p$)=$

E$($p$)=$

$=$

$($b$)$ Suppose a sample of $200$ entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Calculate the sampling distribution of p where p is now the sample proportion of entrepreneurs whose first startup was at $30$ years of age or more. If required, round your answers to four decimal places.

np $=$

n$(1-$p$)=$

E$($p$)=$

$=$

$($c$)$ Are the standard errors of the sampling distributions different in parts $($a$)$ and $($b$)?$

$-$ Select your answer $-$

Justify your answer.

The sample size and the product of p$(1$ p$)$ are

$-$ Select your answer $-$

in both calculations.