Question

1. in a normal distribution with a mean of 45 and a standard deviation of 5, what is the probability that a randomly selected value falls between 45 and 55? 2. in a normal distribution with a mean of 80 and a standard deviation of 8, what is the probability that a randomly selected value falls between 48 and 112?

Explanation:

Step1: Calculate z-scores (Q1)

For $X_1=45$: $z_1=\frac{45-50}{5}=-1$
For $X_2=55$: $z_2=\frac{55-50}{5}=1$

Step2: Find probability (Q1)

Use standard normal table: $P(-1

Step3: Calculate z-scores (Q2)

For $X_1=48$: $z_1=\frac{48-80}{8}=-4$
For $X_2=112$: $z_2=\frac{112-80}{8}=4$

Step4: Find probability (Q2)

Use standard normal table: $P(-4

Answer:

1. The probability is $\boldsymbol{0.6826}$
2. The probability is approximately $\boldsymbol{0.9999}$ (or $\boldsymbol{0.99994}$ for more precision)