"Sunlight makes everyone feel better." To test this claim, 45 college students receive special lights for their bedrooms that slowly turn on in the morning with imitation sunlight. The experiment takes place in January, when it is still dark out in the morning. Prior to participation, the students fill out a questionnaire to measure their general mood. The average score was 2.23. After three weeks with the special light they fill in the questionnaire again. The average score this time was 3.13. The standard deviation of the differences was 0.822.

What is the probability that the difference in average mood scores (after - before) observed is seen or something smaller if the true difference in the scores is 1?

Your answer should express probability as a decimal with no more than two decimal places.