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4 April, 21:02

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 5.3 and a standard deviation of 2.5. Answer parts (a) dash (d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is nothing. (Round to four decimal places as needed.)

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  1. 4 April, 21:48
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    P (X < 4) = 0.3015

    Step-by-step explanation:

    Given:

    - The ratings for current lives on a scale 0 - 10 were normally distributed with parameters mean (u) and standard deviation (s).

    u = 5.3

    s = 2.5

    Find:

    Find the probability that a randomly selected study participant's response was less than 4.

    Solution:

    - Declare a random variable X that follows a normally distribution with parameters u and s, mean and standard deviation respectively.

    X~N (5.3, 2.5)

    - To determine the probability of the rating to be less than 4 for a randomly selected study participant's response we have:

    P (X < 4)

    - Compute the Z-score value for the limit given:

    P (Z < (4 - 5.3) / 2.5)

    P (Z < - 0.52)

    - Use the Z-Table to calculate the above probability as follows:

    P (Z < - 0.52) = 0.3015

    - Hence, the required probability is equivalent to Z-score value probability:

    P (X < 4) = P (Z < - 0.52) = 0.3015
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