The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is under 104? Round your answer to 3 decimal places.

0.977 is the probability  that the average is under 104 for randomly select 64 children.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 100

Standard Deviation, σ = 16

Sample size, n = 64

We are given that the distribution of scores on the MDI is a bell shaped distribution that is a normal distribution.

Formula:

Standard error due to sampling:

P(average is under 104)

Calculation the value from standard normal z table, we have,  

0.977 is the probability  that the average is under 104 for randomly select 64 children.

Step-by-step explanation:

The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.

Here M = 64. The clock gains or losses in a day by

=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)

=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.