In a survey, \( 407 \) people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of \( \$ 45.69 \) and standard deviation of \( \$ 2.05 \) . Estimate how much a typical parent would spend on their child's birthday gift (use a z-interval at a \( 90 \% \) confidence level). Give your answers to \( 2 \) decimal places. Express your answer in the format of \( \overline { x } \pm \) E. 

 

show the work please

Problem \(6 : \) Simple Interest Ania just made \(\$ 1000\) selling her NFT. She plans to invest the money, not touching it for \(10\) years. She plans to invest in a money market at \(3.5 \% \) interest, compounded annually. How much money will she have after \(10\) years? 

HINT: Use the formula Total \(= P ( 1 + r ) ^ { t } \) where P = current value of money, \(r = \) interest rate, and \(t = \) time 

Final Amount in dollars (round to the nearest dollar): 

For the period indicated, calculate a) the amount and b) the compound interest. 

1. The principal of Angelo Carrera's savings account is \( \$ 9,855 \) . It earns \( 6 \% \) interest compounded quarterly for two quarters. 

\( 9855 \times 0.06 \times 0.25 = 147.825 \) 

\( 9855 + 147.825 = 10,002.825\) 

The Wonka Chocolate Factory is sending \( 3 \) of its chocolatiers to attend a 3-day workshop on computer assisted graphics. The daily cost of release time is \( \$ 195 \) per person. The registration fee is \( \$ 95 \) per person. Each designer is also given a \( \$ 50 \) per day miscelianeous allowance. What is the total training cost for the company? 

You travelled to Loompaland for a 3-day conference last week. Your travel expenses include the following: airfare, \( \$ 520 \) ; Uber fare, \( \$ 37.90 \) ; meals, \( \$ 157.90 \) ; hotel, \( \$ 125.90 \) per night for 

\( 2 \) nights; conference registration fee, \( \$ 175 \) . What is your total travel expense? 

Wonkavator Lift Company has some unemployment during the winter months and, therefore, must pay a state unemployment tax (SUTA) of \( 5.4 \% \) . That leaves \( 0.8 \% \) for the federal unemployment tax (FUTA). Compute the federal and state unemployment tax for Charlie Bucket who earns an annual salary of \( \$ 45,365 \) .