Question

A psychology experiment on memory was conducted which required participants to recall anywhere from 1 to 10 pieces of information. Based on many results, the (partial) probability distribution below was determined for the discrete random variable (X = number of pieces of information remembered (during a fixed time period)). What is the missing probability P(X=7)? Your answer should include the second decimal place.

Answer 1

The missing probability is, P (X = 7) = 0.24.

Explanation:

The complete question is:

A psychology experiment on memory was conducted which required participants to recall anywhere from 1 to 10 pieces of information. Based on many results, the (partial) probability distribution below was determined for the discrete random variable (X = number of pieces of information remembered (during a fixed time period)).

What is the missing probability P(X=7)? Your answer should include the second decimal place.

X = # information | probability:

1 | 0.0

2 | 0.02

3 | 0.04

4 | 0.07

5 | 0.15

6 | 0.18

7 | ?

8 | 0.14

9 | 0.11

10 | 0.05

Solution:

The sum of the probabilities of all events of an experiment is always 1.

`\sum\limits^(n)_(i=1){P(X=x_(i))}=1`

Use the above theorem to compute the missing probability.

`\sum\limits^(n)_(i=1){P(X=i)}=1`

`P(X=1)+P(X=2)+P(X=3)+...+P(X=10)=1\\0.00+0.02+0.04+0.07+0.15+0.18+a+0.14+0.11+0.05=1\\0.76+a=1\\a=1-0.76\\a=0.24`

Thus, the missing probability is, P (X = 7) = 0.24.