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Scores from the UCLA Loneliness Scale are normally distributed with a mean of 40 and a...

Scores from the UCLA Loneliness Scale are normally distributed with a mean of 40 and a standard deviation of 10. showing the work, What is the probability that a randomly selected individual from the population will have a score below 30? d. What is the probability that a randomly selected individual from the population will have a score above 60?

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Answer #1

a) P(X < 30)

= P((X - )/ < (30 - )/)

= P(Z < (30 - 40)/10)

= P(Z < -1)

= 0.1587

b) P(X > 60)

= P((X - )/ > (60 - )/)

= P(Z > (60 - 40)/10)

= P(Z > 2)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

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