Answer: 0.0062
Step-by-step explanation:
We assume that the height of a Clydesdale horse is normally distributed.
Let x denotes the height of the Clydesdale horse
Given: Mean : [tex]\mu=72\ inches[/tex]
Standard deviation: [tex]\sigma=1.2\ inches[/tex]
Now, the probability that a Clydesdale is greater than 75 inches tall :
[tex]P(X>75)=P(\dfrac{X-\mu}{\sigma}>\dfrac{75-72}{1.2})\\\\=P(z>2.5)\ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(z\leq2.5)\\\\=1- 0.9937903\ [\text{By z-table}]\\\\=0.0062097\approx0.0062[/tex]
Hence, the required probability is 0.0062.
