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It is given in the question that, the probability of success (p)=$0.50$

Number of trials(n) = $500$

Show that $X$is approximately a binomial random variable.

The random variable $X$is a binomial random variable, which means it has two sides:

• There are two types of successes and failures: going to auction and not going to auction.
• Males are autonomous from one another.
• The number of males is predetermined.
• The probability of selecting a specific person is fixed.

It is given in the question that, the probability of success $\left(p\right)=0.50$

A number of trials$\left(n\right)=500$

Check the conditions for using a Normal approximation in this setting.

The following are the conditions for normal approximation:

$$\begin{gathered} np=500\left(0.5\right) \\ =250>10 \end{gathered}$$

$$\begin{gathered} n(1鈭�p)=500(1鈭�0.5) \\ =250>10 \end{gathered}$$

As a result, the normal binomial distribution approximation might be utilized.

It is given in the question that, the probability of success $\left(p\right)=0.50$

A number of trials$\left(n\right)=500$

Use the Normal approximation to 铿乶d the probability that at least $235$of the men in the sample visit an online auction site at least once a month.

The probability of at least $235$men is computed as:

localid="1650032037644" $$\begin{gathered} P(X鈮�235)=P(Z鈮�\frac{235鈭�0.5\left(1500\right)}{\sqrt{500\left(0.50\right)(1鈭�0.50)}}) \\ =P(Z鈮�鈭�1.34) \\ =0.9099 \end{gathered}$$