Answer:
The value of P (-0.78 < z < 1.16) is 0.6593.
Step-by-step explanation:
A random variable [tex]Z=\frac{X-\,u}{\sigma}[/tex] is said to follow a standard normal distribution if [tex]X\sim N(\mu,\ \sigma^{2})[/tex]. The random variable Z has mean 0 and variance 1.
The probability expression is:
P (-0.78 < z < 1.16)
Use the standard normal table to compute the probability value as follows:
[tex]P (-0.78 <z< 1.16)=P(z< 1.16)-P(z< -0.78)[/tex]
[tex]=P(z<1.16)-[1-P(z<0.78)]\\=P(z<1.16)-1+P(z<0.78)\\=0.87698-1+0.78230\\=0.65928\\\approx 0.6593[/tex]
Thus, the value of P (-0.78 < z < 1.16) is 0.6593.
