Question

9. Find the probability P(140 < x < 149). The μ= 149 and σ= 5.18. Round to 4DP.

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10. Find the probability using the standard normal distribution. Round to 4DP.

P(z < −1.35 or z > 1.35)

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Answer 1

Solution :

Given that ,

9.

mean = = 149

standard deviation = = 5.18

P(140 < x < 149) = P[(140 - 149)/ 5.18) < (x - ) /  < (149 - 149) / 5.18) ]

= P(-1.74 < z < 0)

= P(z < 0) - P(z < -1.74)

= 0.5 - 0.0409

= 0.4591

Probability = 0.4591

10.

Using standard normal table.

P(-1.35 < z < 1.35)

= P(z < 1.35) - P(z < -1.35)

= 0.9115 - 0.0885

= 0.8230

Probability = 0.8230