fill ALLL the blanks On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digitsin the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digitssuccessfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat.A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. Shemeasures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distributionscores is normal.but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with astandard deviation of 1.63 digits.The expected value of the mean of the 49 randomly selected students, M, is v(Hint: Use the population mean and/or standard deviation justgiven to calculate the expected value of M.)The standard error of Mis(Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)The DataView tool that follows displays a data set consisting of 200 potential samples (each sample has 49 observations).Data SetSamplesSampleVariables - 2Observations - 200Statistics for 200 Random Samples (n = 49) drawn from a normal distribution of Digit SpanScoresRwas used to generate the samples.VariablesObservationsТуреObservationsVarlable VForm VValues VMissing VSample MeansQuantitativeNumeric200Sample SDQuantitativeNumeric200VarlableVarlableCorrelationCorrelationSuppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of theDataView tool. The samples are numbered in the first column, and you can use the scroll bar on the right side to scroll to the sample you want.)Use the DataView tool to find the mean and the standard deviation for Sample 133. The mean for Sample 133 isThe standard deviationfor Sample 133 is vUsing the distribution of sample means, calculate the z-score corresponding to the mean of Sample 133. The z-score corresponding to the mean ofSample 133 isUse the Distributions tool that follows to determine the probability of obtaining a mean number of digits successfully repeated greater than the meanof Sample 133.Standard Normal DistributionSendere Cevtent0-3-13The probability of obtaining a sample mean greater than the mean of Sample 133 isIf the sample you select for your statistical study is 1 of the 200 samples you drew in your repeated sampling, the worst-luck sample you could draw is(Hint: The worst-luck sample is the sample whose mean is farthest from the true mean. You may find it helpful to sort thesample means: In Observations view dick the arrow below the column heading Sample Means.)

Question

fill ALLL the blanks On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digitsin the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digitssuccessfully, she will hear five random digits on the next trial. The participant's score is the longest string of digits she can successfully repeat.A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. Shemeasures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distributionscores is normal.but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with astandard deviation of 1.63 digits.The expected value of the mean of the 49 randomly selected students, M, is v(Hint: Use the population mean and/or standard deviation justgiven to calculate the expected value of M.)The standard error of Mis(Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)The DataView tool that follows displays a data set consisting of 200 potential samples (each sample has 49 observations).Data SetSamplesSampleVariables - 2Observations - 200Statistics for 200 Random Samples (n = 49) drawn from a normal distribution of Digit SpanScoresRwas used to generate the samples.VariablesObservationsТуреObservations>Varlable VForm VValues VMissing VSample MeansQuantitativeNumeric200Sample SDQuantitativeNumeric200VarlableVarlableCorrelationCorrelationSuppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of the Suppose this professor happens to select Sample 133. (Hint: To see a particular sample, click the Observations button on the left-hand side of theDataView tool. The samples are numbered in the first column, and you can use the scroll bar on the right side to scroll to the sample you want.)Use the DataView tool to find the mean and the standard deviation for Sample 133. The mean for Sample 133 isThe standard deviationfor Sample 133 is vUsing the distribution of sample means, calculate the z-score corresponding to the mean of Sample 133. The z-score corresponding to the mean ofSample 133 isUse the Distributions tool that follows to determine the probability of obtaining a mean number of digits successfully repeated greater than the meanof Sample 133.Standard Normal DistributionSendere Cevtent0-3-13The probability of obtaining a sample mean greater than the mean of Sample 133 isIf the sample you select for your statistical study is 1 of the 200 samples you drew in your repeated sampling, the worst-luck sample you could draw is(Hint: The worst-luck sample is the sample whose mean is farthest from the true mean. You may find it helpful to sort thesample means: In Observations view dick the arrow below the column heading Sample Means.)

Accepted Answer

As per our guidelines, we are allowed to answer first three sub-parts  
 
Given :
Mean , μ = 7.06…