Help with finding the probability please?

Question

Solve the problem.

A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70.

I just want to double check my answers and I got .0301.

Answer 1

7 - Step Procedure for t Distributions, "one-tailed test"

1. Parameter of interest: "μ" = population mean for true average Math 160 test score

2. Null hypothesis Ho: μ = 70

3. Alternative hypothesis Ha: μ < 70

4. Test statistic formula: t = (x-bar - μ)/(s/SQRT(n))

x-bar = estimate of the Population Mean (statistical mean of the sample) [73]

n = number of individuals in the sample [24]

s=standard deviation [7.8]

μ = Population Mean [70]

5. Computation of Test statistic formula t = 1.88

6. Determination of the P-value: The test is based on n -1 = 23 df (degrees of freedom). Table

"look-up" value shows area under the 23 df curve to the right of t = 1.88 is (approximately) 0.036

7. Conclusion: with significance value α = 0.05 the above shows P-value <= α, [0.036 <= 0.05]. Null hypothesis Ho: μ = 70 should be rejected. Test scores are less than 70 to a significance level of 5%.