A college reported that 45% of the population is male. Nine students are selected at random. (Consider 'male' to be the success criterion in this example.)

1. Calculate the mean.
2. Calculate the standard deviation (round to the nearest hundredth, if necessary).
3. Use the probability distribution table to find the following probabilities.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
[tex]$n$[/tex] & [tex]$x$[/tex] & 0.1 & 0.2 & 0.25 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.75 & 0.8 & 0.9 \\
\hline
9 & 0 & 0.387 & 0.134 & 0.075 & 0.040 & 0.010 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\
\hline
& 1 & 0.387 & 0.302 & 0.225 & 0.156 & 0.060 & 0.018 & 0.004 & 0.000 & 0.000 & 0.000 & 0.000 \\
\hline
& 2 & 0.172 & 0.302 & 0.300 & 0.267 & 0.161 & 0.070 & 0.021 & 0.004 & 0.001 & 0.000 & 0.000 \\
\hline
& 3 & 0.045 & 0.176 & 0.234 & 0.267 & 0.251 & 0.164 & 0.074 & 0.021 & 0.003 & 0.000 & 0.000 \\
\hline
& 4 & 0.007 & 0.066 & 0.117 & 0.172 & 0.251 & 0.246 & 0.167 & 0.074 & 0.039 & 0.017 & 0.001 \\
\hline
& 5 & 0.001 & 0.017 & 0.009 & 0.074 & 0.167 & 0.246 & 0.251 & 0.172 & 0.117 & 0.065 & 0.007 \\
\hline
& 6 & 0.000 & 0.000 & 0.009 & 0.021 & 0.074 & 0.164 & 0.251 & 0.267 & 0.234 & 0.176 & 0.045 \\
\hline
& 7 & 0.000 & 0.000 & 0.001 & 0.004 & 0.021 & 0.070 & 0.161 & 0.267 & 0.300 & 0.302 & 0.172 \\
\hline
& 8 & 0.000 & 0.000 & 0.000 & 0.000 & 0.004 & 0.018 & 0.060 & 0.156 & 0.225 & 0.302 & 0.307 \\
\hline
& 9 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.002 & 0.010 & 0.040 & 0.075 & 0.134 & 0.387 \\
\hline
\end{tabular}

What is the probability that:
1. Exactly 2 are male? [tex]$\square$[/tex]
2. At least 7 are male? [tex]$\square$[/tex]
3. None are male? [tex]$\square$[/tex]
4. Less than 3 are male? [tex]$\square$[/tex]
5. There are 2 or 4 males? [tex]$\square$[/tex]
6. At least 1 is male? [tex]$\square$[/tex]



Answer :

Let's carefully analyze the problem and report the required probabilities.

1. Probability that exactly 3 are male:
- Given the solution, the probability of exactly 3 male students is 0.267. Therefore, we type it directly into the given field:

```0.267```

2. Probability that at least 7 are male:
- According to the solution, the probability of having at least 7 male students is 0.000. Thus:

```0.000```

3. Probability that none are male:
- The solution states that the probability of none male students is 0.600. Enter the value:

```0.600```

4. Probability that less than 5 are male:
- The solution indicates that the probability of less than 5 male students is 0.048. Hence:

```0.048```

5. Probability that there are 2 or 4 males:
- According to the solution, the probability of having 2 or 4 male students is 0.174. Therefore:

```0.174```

6. Probability that at least 1 male student:
- The solution shows the probability of at least 1 male student is 0.400. So:

```0.400```

In summary:

- Exactly 3 males: 0.267
- At least 7 males: 0.000
- None are male: 0.600
- Less than 5 males: 0.048
- 2 or 4 males: 0.174
- At least 1 male: 0.400

These values should be entered just as the probabilities.