Consider the following exponential probability density function.  for x ≥ 0 If needed, round your answer to four decimal digits.(a) Find P(x ≤ 2). (b) Find P(x ≥ 3). (c) Find P(x ≤ 5). (d) Find P(2 ≤ x ≤ 5).

Anull hypothesis states that the difference between 8 hours of sleep and 3 hours of sleep has no effect on the number of pictures a student will remember during a picture memory interface test (pmit). examining the mit database, an extremely small t-value of 0.1611 is found. this t-value is much smaller than the smallest t-value on the chart for p-value reference. from this information we can: select one: a. accept the null hypothesis because the p-value obtained shows that the difference between the two groups being tested is not statistically significant b. accept the null hypothesis because the p-value obtained was statistically significant c. reject the null hypothesis because of the p-value obtained d. reject the null hypothesis because the data obtained is statistically significant