Answer: 0.9972
Step-by-step explanation:
Let x be a random variable that represents the strength of concrete cylinders.
Given: The compressive strengths of 40 concrete cylinders have an estimated mean[tex](\mu)[/tex] of 60.14 MPa and standard deviation[tex](\sigma)[/tex] of 5.02 MPa.
The probability that 10 cylinders will each have strengths between 45 and 75 MPa :
[tex]P(45<\overline{x}<75)=P(\dfrac{45-60.14}{5.02}<\dfrac{\overline{x}-\mu}{\sigma}<\dfrac{75-60.14}{5.02})\\\=P(-3.016<z<2.96)\\\\=P(z<2.96)-P(z<-3.016)\\\\=P(z<2.96)-(1-P(z<3.016))\\\\=0.9985-(1-0.9987)\ \ \ [\text{by p-value table}]\\\\= 0.9972[/tex]
Hence, The required probability = 0.9972
