Question

. A survey found that women spend on average $146 on beauty products during the summer months. Assume the standard deviation is $28. Find the percentage of women who spend less than $160.00. Assume the variable is normally distributed.

Answer 1

Answer:

69.1% of the woman spend less than $160

Step-by-step explanation:

Assuming that the random variable X= spend on beauty products by women during summer months distributes normally , then using the standarized variable Z:

Z= (X - mean / st. dev) = (160.00-146 )/28 = 0.5

then using normal probability tables for Z:

P(X<160)=P(Z<0.5) = 0.691 (69.1%)

thus 69.1% of the woman spend less than $160

Answer 2

Answer: 69.2%

Step-by-step explanation:

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

0.6915 × 100 = 69.2%