Answer:
The correct option is;
0.28
Step-by-step explanation:
The given parameters are;
The mean score for Michael,
= 150
The standard deviation, σ₁ = 30
The mean score for Alan,
= 165
The standard deviation, σ₂ = 15
Taking n₁ = n₂ = 1
![z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%28%5Cbar%7Bx%7D_%7B1%7D-%5Cbar%7Bx%7D_%7B2%7D%29-%28%5Cmu_%7B1%7D-%5Cmu%20_%7B2%7D%20%29%7D%7B%5Csqrt%7B%5Cdfrac%7B%5Csigma_%7B1%7D%5E%7B2%7D%20%7D%7Bn_%7B1%7D%7D-%5Cdfrac%7B%5Csigma%20_%7B2%7D%5E%7B2%7D%7D%7Bn_%7B2%7D%7D%7D%7D)
Taking μ₁ - μ₂ = 0
![z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%28150-165%29%7D%7B%5Csqrt%7B%5Cdfrac%7B30%5E%7B2%7D%20%7D%7B1%7D-%5Cdfrac%7B15%5E%7B2%7D%7D%7B1%7D%7D%7D%20%5Capprox%20-0.577)
The p-value for a z-score of -0.577 from the z-table is 0.28434
Therefore, the probability that Michael, with mean score,
= 150 will have a greater score than Alan, with a mean score of
= 165 is 0.28434 ≈ 0.28
Therefore, the correct option is 0.28