A study of a brand of “in the shell peanuts” gives the following results:

Number of peanut bags Probability

25 0.003
30 0.020
35 0.090
40 0.150
45 0.350
50 0.217
55 0.170

A significant event at the 0.01 level is a fan getting a bag with how many peanuts?


A. 30 peanuts

B. 25 or 30 peanuts

C. 25 or 55 peanuts
D.25,30,55 Peanuts

Answer :D

. 25,30,55 Peanuts

To determine the significant event at the 0.01 level, we need to find the cumulative probabilities for each number of peanuts.

First, let's calculate the cumulative probabilities:

Probability of getting 25 or fewer peanuts:
0.003

Probability of getting 30 or fewer peanuts:
0.003 + 0.020 = 0.023

Probability of getting 35 or fewer peanuts:
0.023 + 0.090 = 0.113

Probability of getting 40 or fewer peanuts:
0.113 + 0.150 = 0.263

Probability of getting 45 or fewer peanuts:
0.263 + 0.350 = 0.613

Probability of getting 50 or fewer peanuts:
0.613 + 0.217 = 0.830

Probability of getting 55 or fewer peanuts:
0.830 + 0.170 = 1

Now, we can compare these probabilities to the significance level of 0.01.

The significant event at the 0.01 level is the first cumulative probability that exceeds the significance level. In this case, it is the cumulative probability of getting 45 or fewer peanuts, which is 0.613.

So, the answer is D. Getting a bag with 25, 30, or 55 peanuts would be a significant event at the 0.01 level.

To determine the significant event at the 0.01 level, we need to find the probability of getting a bag with the specified number of peanuts, and compare it to the threshold of 0.01.

The cumulative probabilities of the bags with different number of peanuts are as follows:

25 peanuts: 0.003
30 peanuts: 0.023 (0.003 + 0.02)
35 peanuts: 0.113 (0.023 + 0.09)
40 peanuts: 0.263 (0.113 + 0.15)
45 peanuts: 0.613 (0.263 + 0.35)
50 peanuts: 0.83 (0.613 + 0.217)
55 peanuts: 1 (0.83 + 0.17)

From the given options, the event that includes the specified cumulative probability at or below 0.01 is option D, which includes bags with 25, 30, and 55 peanuts.

So, the significant event at the 0.01 level is getting a bag with 25, 30, or 55 peanuts.