Answer:
18.5
Step-by-step explanation:
In the above question, we are given the following values
Cumulative probability ( confidence interval) = 0.95 = 95%
Mean = 10.5
Standard deviation = 4.10
We are asked to find the value of x.
To solve for x , we would be using the z score formula.
z score = (x-μ)/σ,
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z score was not given in the question, but we have our cumulative probability as 95%(0.95).
Using the appropriate table,
the z score for 95% confidence is z = 1.96.
Therefore,
z score = (x-μ)/σ,
1.96 = x - 10.5/4.10
Cross multiply
1.96×4.10 = x - 10.5
x = (1.96 × 4.10) + 10.5
x = 8.036 + 10.5
x = 18.536
Approximately to 1 decimal place
x = 18.5
