Use technology or a z distribution table to find the indicated area The masses of eggs collected on a farm are normally distrobuted with a mean of 55 grams and a standard deviation of 4. w grams approximately 80% of the eggs on the farm have a mass greater than which mass

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Complete Question:

Use technology or a z-distribution table to find the indicated area. The masses of the eggs collected on a farm are normally distributed with a mean of 55 grams and a standard deviation of 4.2 grams. Approximately 80% of the eggs on the farm have a mass greater than which mass?

a) 51.5 g

b) 54.1 g

c) 55.8 g

d) 58.5 g

Answer:

d) 58.5 g

Step-by-step explanation:

Using the z score formula

z = (x-μ) / σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question:

x is the raw score is unknown

μ is the population mean = 55 grams

σ is the population standard deviation = 4.2 grams

Where were not given the z score but we were given the probability of the z score to be approximately 80%

Converting 80% to decimal, = 0.80

P (x
Using a normal distribution table, the z score corresponding to 0.80 = 0.8416

Since we have our value for z, we substitute to find x

z = (x-μ) / σ,

0.8416 = (x - 55) / 4.2

0.8416 * 4.2 = x - 55

(0.8416 * 4.2) + 55 = x

x = 58.53472

Approximately = 58.5 grams

Therefore, approximately 80% of the eggs on the farm have a mass greater than 58.5grams.