Question

The mean time that econ 1005 students spend studying statistics is known to be 26.3 hours with a standard deviation of 6 hours. the probability, rounded to four decimal places, that the mean number of hours spent per week studying statistics in a sample of 54 econ 1005 students will be more than 27.1 is:

Answer 1

The probability is approximately 0.98.

To find the probability, we use the z-score formula: Z=
`(X − μ)/((σ/√(n)))` ​,

where:

X is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

In this case, X=27.1, μ=26.3, σ=6, and n=54.

Z =
`(27.1−26.3)/((6/√(54)))` ​

Z =
`(0.8)/((6/7.35))`

Z =
`(0.8)/(0.816)`

Z = 0.98

After calculating the z-score, we use a standard normal distribution table to find the probability.

With a probability of 0.98, there is a moderate likelihood that the mean number of hours spent per week studying statistics in a sample of 54 econ 1005 students will be more than 27.1 hours. This suggests that a significant portion of students may exceed the specified study time.