Final answer:
To find the proportion of scores ≥ a certain value using a histogram, subtract the proportion lower than that value from 1. For scores lower than 75 equaling 0.39, the proportion ≥ 75 is 0.61. Use a graphing calculator for probability calculations.
Step-by-step explanation:
To find the proportion of mathematics test scores that are greater than or equal to a certain value based on a histogram, you subtract the proportion of scores that are less than the given value from 1. For example, given that the proportion of students scoring less than 75 is 0.39, you would calculate the proportion of students scoring 75 or higher by computing 1 - 0.39, which equals 0.61. Thus, the proportion of students with scores ≥ 75 is 0.61.
Calculations of probabilities can be done using a graphing calculator, such as the TI-83+ or TI-84. For instance, to find the probability of scoring more than 24 out of 32 questions correctly, you would use the calculator's function: 1 - binomcdf(32, ½, 24).
The histogram data helps in making decisions about the test scores. If the histogram indicates that the average test score is believed to be more than 65, then at a 5 percent level of significance, we have sufficient evidence to reject the null hypothesis that the mean score is 65. The p-value is a crucial element in hypothesis testing and can be calculated using a graphing calculator.