Question

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally​ distributed, with a mean of 5.2 and a standard deviation of 2.5. Answer parts ​(a)–​(d) below.

Answer 1

The probability that a randomly selected study's participant was less than 4 is 0.2266.

How to compute the probability?

Given that:

mean = 5.8

standard deviation = 2.4

a) P(x < 4) = P[(x - mean ) /sd < (4 - 5.8) / 2.4]

= P(z < -0.75)

Using z table,

= 0.2266

b) P(4 < x < 6) = P[(4 - 5.8)/ 2.4) < (x - \m ) /sd < (6 - 5.8) / 2.4) ]

= P(-0.75 < z < 0.08)

= P(z < 0.08) - P(z < -0.75 )

Using z table,

= 0.5319 - 0.2266

= 0.3053

c) P(x > 8) = 1 - p( x< 8)

=1- p P[(x - \m ) / sd< (8 - 5.8) / 2.4]

=1- P(z < 0.92)

Using z table,

= 1 - 0.8212

= 0.1788

Lastly, there are no unusual events because all the probabilities are greater than 0.05.

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