Find the value of x in X follows normal distribution(5,9/4) where P(X<x)=0.3.
http://davidmlane.com/hyperstat/z_table.html
How can I do this in my calculator
consult your calculator's user guide. probably youtube also has videos.
To find the value of x in a normal distribution where P(X < x) = 0.3, you need to use the cumulative distribution function (CDF) of the normal distribution.
The CDF gives you the probability that a random variable X takes on a value less than or equal to a specified value x. In this case, you want to find x such that P(X < x) = 0.3.
The normal distribution is defined by its mean (μ) and variance (σ^2) or standard deviation (σ). In this case, the normal distribution has a mean of 5 and a variance of 9/4, which means the standard deviation is sqrt(9/4) = 3/2 = 1.5.
To find x, you can use a standard normal distribution table or a calculator with a built-in normal distribution function. The standard normal distribution has a mean of 0 and a standard deviation of 1.
To convert from the given normal distribution with mean 5 and standard deviation 1.5 to the standard normal distribution, you need to standardize x using the formula:
z = (x - μ) / σ
In this case, z = (x - 5) / 1.5
Now, you want to find the z-value corresponding to a cumulative probability of 0.3. In other words, you want to find z such that P(Z < z) = 0.3, where Z is a standard normal random variable.
Next, you can use the standard normal distribution table or calculator to find the z-value that corresponds to a cumulative probability of 0.3. Let's assume the z-value is denoted as z0.3.
Once you have z0.3, you can substitute it back into the formula above to find x:
z0.3 = (x - 5) / 1.5
Rearrange the equation to solve for x:
x = z0.3 * 1.5 + 5
Now, you can calculate the value of x using the z-value obtained from the standard normal distribution table or calculator.