Assuming that the random variable X= spend on beauty products by women during summer months distributes normally , then using the standarized variable Z:
Assuming that the amount that women spend on beauty products during the summer months is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = amount spent.
µ = mean
σ = standard deviation
From the information given,
µ = $146
σ = $28
The probability of women who spend less than $160.00 is expressed as
P(x < 41)
For x = 160
z = (160 - 146)/28= 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.6915
Therefore, the percentage of women who spend less than $160.00 is
