Answer:
Step-by-step explanation:
Let x be the random variable. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 474
σ = 32
x = 514
The probability of being below 514 is expressed as P(x < 514)
For x = 514,
z = (514 - 474)/32 = 1.25
Looking at the normal distribution table, the probability value corresponding to area below the z score is 0.89
Therefore,
P(x < 514) = 0.89
