advertise that they will offer you 100 pounds of free topsoil if it takes their pumpkins more than a certain number of days to grow to maturity. They wish to only have to give away free topsoil AT MOST 2% of the time, and the number of days it takes their seeds to grow to maturity follows a normal distribution with a mean of 106 days and a standard deviation of 5 days. They wish to advertise a number in whole days. What number of days will they advertise

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A company sells pumpkin seeds. They advertise that they will offer you 100 pounds of free topsoil if it takes their pumpkins more than a certain number of days to grow to maturity. They wish to only have to give away free topsoil AT MOST 2% of the time, and the number of days it takes their seeds to grow to maturity follows a normal distribution with a mean of 106 days and a standard deviation of 5 days. They wish to advertise a number in whole days. What number of days will they advertise?HINT: You must round up to ensure that the company requirement that free topsoil is given away no more than 2% of the time is met.

Expert Solution
Step 1

It is given that 

Mean, μ = 106

Standard deviation, σ = 5

Z-Score, Z = ( X - μ )/σ

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