Questions: Per Capita Income of Delaware Residents In a recent year, Delaware had the highest per capita annual income with 51,803. If σ=4850, answer the following questions. Assume that the sample is taken from a large population and the correction factor can be ignored. Round intermediate z-value calculations to two decimal places and the final answers to at least four decimal places. Part 1 of 2 What is the probability that a random sample of 36 state residents had a mean income greater than 50,200 ? P(X̅>50,200)=.976 Part: 1 / 2 Part 2 of 2 What is the probability that a random sample of 36 state residents had a mean income less than 48,800 ? P(X̅<48,800)=

Transcript text: Per Capita Income of Delaware Residents In a recent year, Delaware had the highest per capita annual income with $\$ 51,803$. If $\sigma=\$ 4850$, answer the following questions. Assume that the sample is taken from a large population and the correction factor can be ignored. Round intermediate $z$-value calculations to two decimal places and the final answers to at least four decimal places. Part 1 of 2 What is the probability that a random sample of 36 state residents had a mean income greater than $\$ 50,200$ ? \[ P(\bar{X}>50,200)=.976 \] $\square$ Part: $1 / 2$ Part 2 of 2 What is the probability that a random sample of 36 state residents had a mean income less than $\$ 48,800$ ? \[ P(\bar{X}<48,800)= \] $\square$