### Expert Answer:

The value of $p$ can be calculated by using a standard normal table: This standard normal table gives the value of z-test statistics, which is: \[z= 1.74\] Null hypothesis is represented by $H_o$. The given value of $p$ for $H_o$ test is: \[p= 0.5\] We have to find the $z$-test statistics value when the $p$-value for the alternating hypothesis is given as: \[H_a: p>0.5\] The value of $z$ statistics tells us the kind of test. For example, in this question, if the value of $z$ statistics is $-1.74$, then the test is a left tailed test. On the other hand, if the value of $z$ is $1.74$, then the test is called the right tailed test.**Numerical Results:**

The formula for right tail test is given as:
\[p = 1 – P (Z > z)\]
By putting given values:
\[p = 1- P (Z > 1.74)\]
The standard probability table will be used to find the value of $p$ at $1.74$ .
By putting values from the table, we get:
\[p = 1- 0.9591\]
\[p = 0.0409\]
The value of $p$ is $0.0409$ for $H_a$: $p$ > $0.5$.
**Alternate Solution:**

We can also find the value of $p$ by simply looking at the standard probability table. It includes two steps:
Step 1: Look out for $1.74$ from the rows.
Step 2: Look out for the value of $p$ against the row of $1.74$.
The value of $p$ will be $0.0409$.
### Example:

If the $p$-value is less than 0.5, that is $p$ < $0.5$, then we will take the left tailed test where the null hypothesis is given as: \[H_o: p = 0.5\] The value of $p$ for alternating hypothesis is: \[H_a: p < 0.5\] The formula for $p$-value is given as: \[p = P ( Z < z)\] By putting values in the above formula: \[p = P ( Z < -1.74)\] by using standard probability table to find the $p$-value at $-1.74$: \[p = 0.0409\]*Image/Mathematical drawings are created in Geogebra*

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