the mean number if calories ingested per day for females age

the mean number if calories ingested per day for females aged 25 is 2750, with a standard deviation of 276. If a simple random sample of 100 females is selected, what is the probability that the mean number of calories ingested is more than 2800?

Solution

the mean number if calories ingested per day for females aged 25 is 2750, with a standard deviation of 276. If a simple random sample of 100 females is selected, what is the probability that the mean number of calories ingested is more than 2800?

Standard error = sd/sqrt(n) =276/sqrt(100) =27.6

Z value for 2800, z=(2800- 2750)/27.6 =1.81

P( x > 2800) = P( z > 1.81) = 0.0351

The required P= 0.0351